In this paper, we have simulated the excitation of wake fields in the interaction of an intensive laser pulses having Half-Sine and Gaussian time envelopes with a fully ionized cold plasma using particle in cell (PIC) method. We investigated the dependency of wake filed amplitude to different laser and plasma parameters such as laser wavelength, pulse duration and electron number density. In addition, the effect of employing a longitudinal magnetic field on the intensity of wake field is studied. It has been seen that the wake field intensity is enhanced in the presence of a magnetic field for both Half-Sine and Gaussian shape pulses. Our aim has been finding optimum values of different parameters for which higher accelerating wake electric fields can be obtained.