HF wave propagation in the turbulent stratified ionosphere is investigated using the multiple phase-screen simulation method. For waves incident along the axis of the background stratification, generalized parabolic equations for the modified complex amplitude u are derived which are applicable even in the strong scattering case. Based on these parabolic equations, several one-dimensional random phase screens are numerically generated to represent the effect of the random irregularities on the wave. For plane wave incidence, various statistical properties of the field, such as correlation, power spectrum, scintillation index, etc., can be directly computed using spatial averaging under the ergodicity assumption. The simulation method is also used to examine the effect of the velocity profile on the drift pattern on the ground.