The generation of half-cycle unipolar pulses upon reflection of a femtosecond laser pulse from a plasma mirror was theoretically studied. Numerical simulations were used to compare the quasi-static model and the Ammosov-Delone-Krainov (ADK) model. It was shown that the leading edge of the pulse ionizes the medium, forming a plasma layer, while the trailing edge is reflected from it, generating a quasi-unipolar half-cycle pulse. Qualitative agreement between the pulse shapes was found, despite minor differences in amplitude. The results are important for the development of methods for sub-cycle control of light and the study of nonlinear processes in plasma. Keywords: nonlinear ionization of atoms in a strong light field, tunnel ionization, plasma mirrors, half-cycle pulses, unipolar pulses, attosecond physics, extremely short pulses.