A new construction of the microwave-pumped laser based on the light-pumping cell that uses radiation of sulfur vapor exposed to electromagnetic waves of the microwave band is described. Advantages of this design are the simple structure, high efficiency of the optical pumping cell, the possibility of cooling the pumping element, and easiness of modifying the emission spectrum of the optical pumping by changing the chemical composition of admixtures in the sulfur light-emitting cell. A mathematical tool for the simulation of the short-pulse operation of the microwave-pumped laser is proposed basing on the generalized wave equation solving for a regular transmission line with essentially nonlinear dispersion characteristic and substantial dissipation. Possible techniques for the numerical solving the generalized wave equation are discussed.