Analytical solutions for a continuum model of a DC gas discharge were obtained by asymptotic approximations. The solutions are one-dimensional and stationary. Three different cavity configurations of electrode pairs were considered, namely, parallel flat plates, concentric cylinders and concentric spheres. The asymptotic approximations consider nonlinear effects that are present in the dynamics of the plasma which are neglected in most of analytical solutions found in the literature. The obtained solutions determine the distribution of positively and negatively charged particles, as well as the electric potential along the space domain. Analytical results agree quantitatively with results from a spectral numerical solution developed for validation purposes. Such agreement was possible in a regime where the rate of charged particle production was assumed to be very small. Finally the limits of this regime are reported.