We have conducted particle-in-cell (PIC) simulations of a linearly polarized intensive laser pulse with two different envelopes propagating through a homogeneous fully ionized cold plasma. It is shown that the amplitude of the wake field depends on laser wavelength, pulse duration, electron number density and envelope shape. We have also simulated the effect of applying a longitudinal magnetic field on the wake field excitation process. It is observed that magnetic field enhances the wake field and increases its intensity in all cases. Our results are in agreement with the analytical results presented by Askari and Shahidani [Opt. Laser Technol.45, 613–619 (2013)] and can help choosing the optimum values of affecting laser and plasma parameters in order to reach high accelerating wake electric fields.