Effect of noise and detection error is one of three important factors affecting the performances of an adaptive optics (AO) system. In an AO system, noise and detection error can produce errors in the tilt detection of a Hartmann Shack (H S) wavefront sensor and have further effects on the performance of the AO System. A theoretical model of numerically simulating the effects of noise and detection error is presented and a computer program has been compiled, which is combined with our existing program of numerical simulation of the laser propagation in turbulent media and an AO system. The effects of detection error, readout noise and photon noise on a practical AO system have been namerically simulated. The results are quite useful for the design of a practical AO system.