After landing B757-200 flight crew parked their aircraft on a parallel taxiway when they received a L HYD SYS PRESS EICAS warning. They were subsequently towed to the gate for maintenance.

Narrative

Upon exiting runway the ECAM displayed L HYD SYS PRESS. The Captain made a left turn onto the parallel taxiway and stopped the aircraft. I requested CFR assistance and then read the associated QRH checklist. We performed the items in the checklist and then shut down the left engine. While waiting for CFR to arrive we had the flight attendants check out the left side of the windows for any damage or indication of fire. We then asked Operations for Maintenance assistance and a tow in. CFR informed ATC who then informed us that our aircraft looked normal but that there were marks on the taxiway where we exited the runway. We later determined that those were black tire marks which were the result of the left main tires being wet with hydraulic fluid. Maintenance advised we had a broken Thrust Reverser Actuator on the left engine and it was leaking hydraulic fluid. The right engine was shut down and we were towed to a maintenance hard stand from which our passengers were bussed back to the main terminal.