The excitation of plasma waves by a short pulse of focused laser radiation is studied. Since the excitation of waves depends strongly on the pulse form, we described in detail its form and the conditions when the expression for the pulse field is applicable. Limitations on the pulse duration and the degree of laser radiation focusing are given. The basis for studying the excitation of plasma waves is the equation for potential electric fields. This equation describes the dispersion, weak damping due to collisions of electrons with ions, and wave excitation due to the ponderomotive effect of a short pulse of laser radiation. The dispersion of waves is described by a small integral term that takes into account the thermal motion of electrons. The effect of electron collisions on the damping of waves is described by the Fokker-Planck collision integral. The expression for the ponderomotive force is written taking into account the fact that the laser pulse propagates with a group velocity close to the speed of light. From the equation for waves, we find the Fourier transform of the electric field, which makes it possible to analyze the spectral composition of the excited waves and their radiation patterns. When radiation is weakly focused, waves are excited along the direction of laser pulse propagation. In the case of strong focusing, plasma waves are excited at an angle to this direction, and the greater the angle magnitude, the greater the difference of wave frequency from the electron plasma frequency.