Means for estimating the wheel torque

A transmission control system for a vehicle having an engine with an output shaft, a torque converter, a stepped automatic transmission mechanism, and a clutch for engaging and releasing a plurality of gear shafts and input/output shafts with each other so as to change a shift change ratio by operation of the clutch. The control system produces a shift signal output indicating a shift change ratio of the stepped automatic transmission mechanism, detects an input torque of the stepped automatic transmission, recognizes an actual mechanical shift start timing of the stepped automatic transmission mechanism and changes engaging pressure on the clutch in accordance with a manipulation variable. An input torque-manipulation variable relationship between the input torque and the manipulation variable for every shift change ratio indicated by every shift signal and every mode of shift change ratios is stored. A manipulation variable calculation is performed when the shift signal and the shift signal output changes and the actual mechanical shift start timing is recognized.