Date: 201603
Local time of day: 1801-2400
Location: ZZZ.Airport, US
Flight conditions: VMC
Light: Night
Aircraft: B737 Undifferentiated or Other Model
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Mission: Passenger
Flight phase: Taxi
Reporter organization: Air Carrier
Reporter function: Pilot Not Flying; Captain
Reporter qualification: Flight Crew Air Transport Pilot (ATP)
Human factors: Communication Breakdown; Distraction
Second reporter function: First Officer; Pilot Flying
Anomaly: Deviation / Discrepancy - Procedural Published Material / Policy; Ground Event / Encounter Other / Unknown
Detector: Person Flight Crew; Person Ground Personnel
When detected: Taxi
Result: Flight Crew Became Reoriented; General Maintenance Action
Contributing factors: Human Factors
Primary problem: Human Factors

Narrative: During pushback we were given clearance to start both of our engines from the pushback crew. I gave the First Officer the command to start the #2 engine. As the pushback crew brought the airplane to a halt during a routine SOP pushback; I heard 'set brakes' via the Flight Interphone System; I responded with; 'brakes set' and as I said this my First Officer brought my attention to an ACARS message we had just received stating something similar to 'flight number not recognized.'My First Officer stated something to the fact that he wasn't sure why we were receiving that ACARS message. The next thing I heard was 'brakes; brakes; brakes!' via the Flight Interphone System. I immediately applied full brakes and felt the airplane slightly jerk. The pushback personnel informed me that the airplane had rolled forward up against the handle of the tow bar.I set the parking brake and shut down the #2 engine (#1 engine had not yet been started). I had a brief discussion with the pushback personnel that there were no injuries and no obvious damage; but the tow bar was stuck due to the nose tire being up against it. We contacted maintenance and multiple maintenance personnel quickly appeared and inspected the situation.I was informed by maintenance personnel that they had installed the bypass pin; disconnected the handle from the tow bar; pulled the tow bar handle out from being stuck against the nose wheel; and reattached the handle to the tow bar. Multiple maintenance personnel inspected the tow bar; nose wheels; tires; steering and nose gear. We conducted steering tests; and re-inspected the nose tire. Maintenance could find no damage with any items.Maintenance did not want to write up any discrepancy because they said there was no discrepancy to write up. We also did not write up any discrepancy due to advice from maintenance personnel. We then continued an SOP pushback; disconnect and release and taxied out to the runway with no further issues; and continued the flight to the final destination.Although I am uncertain; I can think of only two possibilities that could have caused this. Either the parking brake somehow got released or I never got the parking brake set after pushback. I would guess it was the latter. We were very fortunate that there were no injuries or damage. I also feel very fortunate to have a pushback crew that was very alert and communicated; 'brakes; brakes; brakes!' in such a timely manner.


Second narrative: [Report narrative contained no additional information.]


Synopsis: During pushback brakes were not set as ground crew disconnected the tow bar. Aircraft rolled into the tow bar before stopping.