Recently, by the development of finite element methods it has become able to analyze the kinematic boundary value problems of continuum materials. In these situations, to find suitable constitutive equations is eagerly requested. In compliance with these requests, many studies on elastoplastic constitutive equations not only for metals but also for granular materials like soils have been actively advanced and many reports have been presented. By the way, the smooth c ontinuous transition processes from elastic (sub-yield) states to plastic (yield) states shown in experimental results cannot be expressed by the usuaI constitutive equations, because in these equations the kinematic state of materials is distinctly divided into an elastic state and a plastic state. This is one of large defects included in the usual constitutive equations. On the other hand, the authers have proposed a new plastic constitutive equation taken account of this continuous transition process (Hashiguchi and Ueno, 1977). In this equation, it is assumed that a plastic deformation occurs from the beginning of deformations, i. e., the plastic deformation always occurs in loading process. Now, the plastic strain increment in loading processes is defined as follows. dε^p_<ij>=Mdf/(dF)/dε^p_v((∂f)/(∂P)-N)(∂f)/(∂σ_<ij>) where f is a loading function, F is a hardening function, r is a current plastic volumetric strain, σ_<ij> is a current stress, P is a mean stress, M and N are functions of the parameter f/F(0 ≦ f/F ≦ 1). M and N control the magunitudes of plastic strain increments, especially N is useful for the expression of a strain softening behavior. In this paper, the new plastic constitutive equation mentioned above was employed to the formulation and the programming of the finite element method for analyzing boundary value problems of elastoplastic deformations of granular materials. Two examples of axisymmetric compression processes were analyzed by this finite element method and compared with experimental results of Weald clay (Parry, 1959) and Toyoura sand (Miura, 1975), and further compared with analytical results calculated by the usual method. These comparisons show t h at this finite element method gives more suitable values to experimental results than the usual method and expresses fairly well the characteristics of transition processes. Therefore, it seems that this finite element method is capable to analyze adequately the general boundary value problems. Hereafter, we shall analyze practical problems for agricultural machinery, e. g., a sinkage problem of tractor wheels by use of this finite element method.