A technique is developed for the treatment of space-time neutron kinetics, which can include the effects of material motion. The new method is applied to sample problems where azimuthal fuel motion is postulated to occur. The technique developed employs the finite element method, Gear's variable predictor corrector scheme, and a Lagrangian mesh that moves with the reactor materials. We treat a cylindrical reactor in (r,θ) geometry. Because finite elements are used to describe both the fluxes and the boundaries of the mesh elements, the resulting deformed elements could be arbitrarily shaped. Second-order polynomials (elements) were found to be better than linear polynomials in treating the geometry because of the curved boundaries used in the problem. Azimuthal motion was found to increase reactivity, and large motion resulted in large increases in reactor power for the cases studied. However, the cases studied showed that azimuthal motion was less important than both inward and outward radial motion. Point kinetics (based on first-order perturbation theory) did not accurately predict the power excursion in cases where substantial azimuthal displacement occurred.