Its unclear if their unarmed attack counts as an attack, which can be used to take the Shove action.m
Yes you can since you you can use one of your multiple attacks with the Attack action to shove, which you do when using Martial Arts.
PHB78 Martial Arts: When you use the Attack action with an unarmed strike or a monk weapon on your turn, you can make one unarmed strike as a bonus action.
PHB195 Shoving a Creature: Using the Attack action, you can make a special melee attack to shove a creature, either to knock it prone or push it away from you. If you’re able to make multiple attacks with the Attack action, this attack replaces one of them.
Plaguescarred wrote:
Plaguescarred wrote:
The answer is not with the bonus action, but yes, if you use the Attack action, as one of your attacks with that attack (which triggers the bonus action, sure, but isn't) may be replaced with a shove.
So, as long as the shove comes from one of the Attacks (urnarmed or no), it's legal.
So not 100% as much utility as allowing the bonus action to do it (which would be a clear houseruling) but still allows you to be attacking and shoving in the same turn.
reddaemon wrote:
Whatever the precise rules might suggest, it seems to me interchanging a shove for an attack, would be well within the "improvised actions" rule. And an easy one to adjudicate , since all the rules are already there. Is there any real benefit to say having 3 attacks plus a bonus action attack, and using the bonus action to knock prone, as opposed to one of the 3 normal attacks? If the target is knocked prone, you'll get 3 attacks on him with advantage either way.
Strictly, no, you cannot use a Martial Arts, Flurry of Blows, or any bonus action attack to "Shove" (or "Grapple").
A character can Shove or Grapple with the Extra Attack feature, because it enhances the "Attack" action, which is the prerequisite for Shoving or Grappling. (It's also explicitly allowed in the rules for these attacks.)
Way of the Open Fist monks can add a trip effect or forced movement to their Flurry of Blows, and Battlemaster Fighters can choose to use a Maneuver on bonus action attacks, but these are special abilities.
That being said, it is of course possible to Shove or Grapple on your normal "Attack" (or "Attacks"), and then use your Flurry of Blows, Martial Arts, off-hand attack, or Polearm Mastery to make a regular melee attack.
I mispoke let me clarify. What i meant is that when you use the Attack action with an unarmed strike using Martial Arts, you should be able to make a special melee attack to Shove instead of a regular attack. When doing so, you can make one unarmed strike as a bonus action.
EDIT But looking at Martial Arts Attack again, i blieve its not possible because the Attack action used to Shove is not made with an unarmed strike, which means you cannot make one unarmed strike as a bonus action. Its a technical detail preventing it and i'm sure you ask one of the Devs and he'll say you can... 
FWIW for comparison's sake, based on the wording provided by blackmetal (i'm away from my books), compared to Martial Arts, the Warpriest could use its Attack action to Shove, and a bonus action to attack since its Attack action doesn't have to use a weapon.
blackermetal wrote:
Plaguescarred wrote:
The Monk's bonus action attack is explicitly an Unarmed attack. You can only make an Unarmed attack with it - period. You can't even substitute in a Monk weapon for that attack. This is an important distinction because while you may have a magical, +1, or silvered Monk weapon (ie Short Sword) your unarmed attack does not necessarily have those things.
Furthermore, in order to gain access to that bonus action attack you have to of used your action to make an attack with a Monk Weapon or Unarmed attack. So once you get extra attack you could Action - Attack: Shove + Attack, them Bonus Action Unarmed attack, but until then if you don't include an monk attack in your action you don't get that unarmed attack.
A shove counts as an Attack for the sake of the Attack action. But you can only shove on the Attack action, not the bonus action of Flurry of Blows.
TLDR: You can shove on the initial attack action, but the followup flurry of blows can only be strikes.
Yunru wrote: