Simple question, can a Monk/Rogue make an Unarmed Strike then use Sneak attack with that strike?

I would argue that a Monk's Unarmed Strike would be considered a Finesse weapon due to the fact that a Finesse weapon can use either your STR or DEX modifier as shown in the official rules below as well as the official rule of Monk stating the exact same thing for their Unarmed Strikes:

Finesse. When making an attack with a finesse weapon, you use your choice of your Strength or Dexterity modifier for the attack and damage rolls. You must use the same modifier for both rolls.

Martial Arts

At 1st level, your practice of martial arts gives you mastery of combat styles that use unarmed strikes and monk weapons, which are shortswords and any simple melee weapons that don't have the two-handed or heavy property.

You gain the following benefits while you are unarmed or wielding only monk weapons and you aren't wearing armor or wielding a shield:

• You can use Dexterity instead of Strength for the attack and damage rolls of your unarmed strikes and monk weapons.

And of course there's the rules on the Sneak Attack:

Sneak Attack

Beginning at 1st level, you know how to strike subtly and exploit a foe's distraction. Once per turn, you can deal an extra 1d6 damage to one creature you hit with an attack if you have advantage on the attack roll. The attack must use a finesse or a ranged weapon.

You don't need advantage on the attack roll if another enemy of the target is within 5 feet of it, that enemy isn't incapacitated, and you don't have disadvantage on the attack roll.

The amount of the extra damage increases as you gain levels in this class, as shown in the Sneak Attack column of the Rogue table.

Let me know what you think, thanks in advance.

RAW, they can't, because Martial Arts allows you to use your Dex for attack and damage rolls with unarmed strikes but they still don't have the Finesse property.

Personally, I think it should still be allowed, it's hardly an overpowered combination and I've felt that 5E's version of Sneak Attack is too restricted.

Having Dexterity as the governing attribute for a weapon doesn't make it Finesse. Since it doesn't specify that it's Finesse, it's neither Finesse nor Range, so it doesn't qualify for a Sneak Attack.

Of course, what the DM says goes at their table. I've not looked into the Monk and Rogue subclasses enough to offer an opinion on whether it should be allowed.

I don't think there's anything massively gamebreaking to it; a Monk can squeeze in a few more attacks than a TWF Ranger of the same level, but that's arguably getting hit with diminishing returns, and the Rogue's Steady Aim feature from Tasha's uses the Bonus Action, so they're demonstrably not doing anything a Ranger can't in that scenario. Not seeing anything else in the class that really jumps out either.

Quote from DruidVSAdventure >>

Simple question, can a Monk/Rogue make an Unarmed Strike then use Sneak attack with that strike? 

 The reasons Sneak Attack doesn't work on unarmed strikes is because they're not finesse or a ranged weapon. Here's an official ruling in Sage Advice Compendium explaining in more details:

Can a rogue/monk use Sneak Attack with unarmed strikes? The Sneak Attack feature works with a weapon that has the finesse or ranged property. An unarmed strike isn’t a weapon, so it doesn’t qualify. In contrast, a rogue/monk can use Sneak Attack with a monk weapon, such as a shortsword or a dagger, that has one of the required properties.

I've been against this in the past but am kind of on the fence about it. I don't like it mainly because of the dipping issue, either monk dipping rogue or rogue dipping monk. But like I've said, I'm on the fence about it and could see allowing it. Just rubs me the wrong way for some reason. Maybe because monk has always been my favorite class since AD&D.

Yeah, I get the idea that the two could stand to just stay in their lanes. Wouldn’t hold it against a DM to not make an exception, just an observation that in practice it plays about the same as a melee Ranger dip.

Even if your unarmed strikes were finesse, they still wouldn't be weapons. U can use them to make weapon attacks, but they still are not weapons. I for one would love to do an unarmed rogue build for a sort of batman vibe, but I would understand that I would need to bend the RAW. However, the main goal of DND is to have fun. The DMG even states "the DM interprets the rules and decides when to abide by them and when to change them." I know my DM would be just fine with this, but I'm not expecting to be allowed to play an unarmed rogue in a adventurers league game.

You can't combine sneak attack and unarmed strikes, but monks can still use weapons just fine, including several finesse and ranged ones. So if the ask is to combine monk and sneak attack rather than unarmed strike and sneak attack, the former is doable quite easily.

Purely RAW, it isn’t Finesse, and therefore cannot. But as a DM I wouldn’t have a problem with it!