A new dynamical core is developed based on the elastic, non-hydrostatic equations of motion using a hybrid vertical coordinate. A height-based, terrain-following coordinate is used near the surface which smoothly transitions to a quasi-Lagrangian (isentropic) coordinate in the free atmosphere. Integral constraints such as total energy and angular momentum conservation are preserved by the vertical differencing scheme. The dynamics are tested in a model which is a prototype for a future global cloud resolving model. Test results on various spatial scales are presented.