The objective of this study is threefold: (1) to formulate an elastoplastic constitutive model that portrays cyclic response of geomaterials, (2) to develop an algorithm for numerical implementation, and (3) to verify the applicability of the developed model to cyclic behavior. Geomaterials exhibit characteristic hysteresis responses under cyclic loading. For instance, alternation of stiffness degradation and recovery associated with plastic volumetric contraction and expansion is observed under undrained cyclic shear. Furthermore, strong pressure dependence of the elasticity modulus in geomaterials is well known, and thus hypoelasticity, namely rate-type elasticity, is widely used in existing elastoplastic models. However, hypoelasticity does not guarantee energy conservation property in elastic responses. In this study, the Cam-clay model is formulated on the basis of hyperelasticity to resolve the issues concerning the hypoelasticity. The model is extended by introducing the concept of subloading surface, together with the rotational hardening, in which a tensorial internal variable, called the elastic-core tensor, is incorporated to be applicable to cyclic loading. Furthermore, we develop the implicit stress calculation algorithm utilizing the return mapping scheme, and it is implemented into a numerical code. A simulation of a triaxial test for a sand is presented to demonstrate the performance of the developed model. We also assess the efficiency and robustness of the numerical algorithm.