A new elastoplastic model called loading memory surface based on the critical state concept and the multi-surface framework is proposed for geomaterials. The model uses a hypoelastic formulation and two plastic mechanisms. The formulations of the model are made in three-dimensional stress–strain space and work under both monotonic and cyclic loadings. A newly introduced formalism makes it possible to obtain the cyclic response directly from the monotonic loading one. This formalism gives a three-dimensional generalization of the well-known Masing rule. The model has been validated against test results of Hostun sand under several conditions: monotonic and cyclic, drained and undrained, tests in compression and in extension, and at different confining pressures and different densities. Copyright © 2014 John Wiley & Sons, Ltd.