The geometrical nonlinear dynamic response of sandwich beams is studied using a dynamic high-order nonlinear model. The model is derived using the variational principle of virtual work and uses the Extended High-Order Sandwich Panel Theory approach with consideration of two interfaces between the three layers. A first-order shear deformation theory is adopted for the face sheets, while the kinematic assumption of high-order small deformations that account for out-of-plane compressibility are considered for the core layer. The nonlinearity of the dynamic model is introduced by considering geometrically nonlinear kinematic relations in the face sheets. The nonlinear kinematic relations and the dynamic modeling aim to evaluate the effects of the two features and their coupling on the response. The nonlinear dynamic response of sandwich beams is studied through two numerical cases and comparison of the nonlinear results with their linear counterparts. The first case looks into the coupling of the global geometrical nonlinear behavior with the dynamic behavior. The second case focuses on the local instability of the face sheets and its interaction with the compressibility of the core in the dynamic response of soft core sandwich beams. The comparison of linear and nonlinear dynamic response in the two cases sheds light on the coupling of the geometrical nonlinear and dynamic behaviors. Among other features, the latter is expressed by nonlinear attractors, higher modes response, nonlinear frequency response, and significant wrinkling response.