Several Cam-clay models have been formulated in the framework of finite deformation elastoplasticity based on the multiplicative decomposition of the deformation gradient and using hyperelastic constitutive law. However, previous studies have not fully considered the volume change of the intermediate configuration. Due to this, these formulations cannot guarantee the existence of the state boundary surface in Cauchy stress - specific volume space, which is important for the derivation of Cam-Clay model. Therefore, this study reconstructs Cam-clay model that can explain the existence of the state boundary surface. For this purpose, constitutive equations are formulated by considering the plastic volume change referring to Bennet et al. (2016). Moreover, after constructing an implicit stress update algorithm and deriving the tangent coefficient consistent with it, this model is applied to an incremental analysis using FEM. As a verification of the proposed model, a simulation of a triaxial compression test was performed, and the same results as the drainage triaxial compression test of reconstituted regular consolidation soil were obtained. Additionally, to demonstrate the significance of the proposed model, comparisons with an existing model using Kirchhoff stress were performed. The results indicated that the proposed model could consider the experimental facts that are fundamental to the critical state soil mechanics.