Bergeron first suggested that atmospheric frontogenesis is caused by horizontal wind deformation fields acting on pre-existing horizontal temperature gradients. A three-dimensional time-dependent mathematical model of the atmosphere which incorporates this process through the initial conditions and boundary conditions is formulated. Dissipative processes are neglected and the equations are approximated by assuming that the Richardson number is initially large. The resulting equations are then solved analytically. The solution shows, under certain conditions, fronts developing with properties similar to many atmospheric fronts, thereby giving support to Bergeron's hypothesis.