An initially discontinuous density distribution (the shock‐tube configuration) is studied analytically as an initial value problem for the Boltzmann equation. The distribution function is expressed in an infinite series of orthogonal polynomials in velocity space. The early time behavior is dominated by a collisionless interaction; the weight function for the orthogonal polynomials is, therefore, taken as the distribution function corresponding to the collisionless evolution of the density discontinuity. Moment equations are developed for Maxwell molecules. Truncation of the series for the distribution function leads to a determinate system of six quasilinear partial differential equations for the first six moments. For sufficiently small initial number density ratio the system is totally hyperbolic with the characteristics determined from the known collisionless solution. Numerical solutions are obtained for initial number density ratios of 5, 10, and 100. Early time results show the departure from collisionless behavior; moreover, after a sufficient time, the shock, contact, and expansion regions become evident as in the classical case. The shock region evolves into a steady‐state shock wave with structure similar to that obtained by steady‐state theories. The contact and expansion regions also assume their expected asymptotic character.