Using the analogy with stationary axisymmetric solutions, we present a method to generate new analytic cosmological solutions of Einstein’s equation belonging to the class of T3 Gowdy cosmological models. We show that the solutions can be generated from their data at the initial singularity and present the formal general solution for arbitrary initial data. We exemplify the method by constructing the Kantowski–Sachs cosmological model and a generalization of it that corresponds to an unpolarized T3 Gowdy model.