An A319 Captain describes a noticeable 'shudder' that was detected during taxi-out with both engines running; while exercising the pitch and lateral controls. The same 'shudder' was also felt by the cabin crew.

Narrative

Flight control check during taxi-out with both engines running; a noticeable 'shudder' was detected by the flight crew while exercising the pitch and lateral controls. The shudder was felt by the cabin crew also. The flight controls moved correctly but repeated flight control movement caused the shudder to re-occur. After notifying Dispatch by ACARS of the problem; a three-way conference call was established with the PIC; Dispatch and Maintenance Control. While stationary on the ramp with parking brake set; Maintenance Control suggested we turn ELACs 1+2 and all three hyd pumps to 'off.' After 10 seconds; we restored hyd pumps and ELACs. A similar 'shudder' was felt when the hyd pumps were turned to 'on.' After that; we exercised the pitch and lateral flight controls and the same shudder event occurred. Maintenance Control and Dispatch recommended return to gate which we did. Maintenance arrived at the aircraft and various 'byte' tests and systems checks were accomplished. The 'shudder' event was confirmed by Maintenance although no abnormalities were shown by computer diagnostics. After 45 minutes of analysis; Maintenance started both engines at the gate. The flight controls were exercised. The 'shudder' had disappeared. After further discussion with Maintenance; Maintenance Control; Dispatch and the PIC; the aircraft was determined to be airworthy.The flight departed the gate and proceeded without difficulty. At destination during taxi-in and also at the gate; with both engines running; flight control checks were accomplished by the flight crew. The checks were normal without any of the shudder detected 6 hours earlier. Not completely sure what caused the 'shudder' event while exercising the flight controls. Careful checking of flight controls before flight is certainly an important element of safe operation. There was good coordination between Maintenance; Maintenance Control; Dispatch; Operations and the flight crew; while the problem was being addressed.