The aim of this work is to simulate the forming process of green anodes. For this purpose, a nonlinear compressible viscoplastic constitutive law is presented. The concept of natural reference configuration is considered. Within an isothermal thermodynamic framework, a Helmholtz free energy is proposed to take into account the nonlinear compressible deformation process occurring between natural reference configuration and current configuration. A dissipation potential is introduced in order to characterize the irreversible aspect of compaction process. The constitutive law is thus formulated through two equations: (1) an expression of Cauchy stress tensor and (2) a differential equation characterizing the evolution of the natural reference configuration. Material parameters are assumed to be a function of the apparent green density. An experimental study is carried out in order to characterize the compaction behavior of the anode paste. A user's material VUMAT subroutine for finite-element dynamic explicit analysis has been developed and implemented in the abaqus commercial software. To evaluate the model predictive capability, numerical simulations of the compaction forming process of anode paste were performed. Simulation results show that the constitutive law predicts the experimental trends and gives insight of physical responses. This constitutes a first step toward characterizing the anode paste behavior and making a benchmark with experimental results on the forming process of anode paste.