We have calculated three-dimensional (3-D) stresses and strains, and bulk density of cohesionless granular material using the distinct element method. Based on these data, 3-D stress and strain relations have been calculated, and constitutive equations for granular materials have been derived. Our 3-D constitutive equations cover the elastic, plastic and flow regions. A1-A4, which are strain size functions for each strain component, and nonlinear parts in the constitutive equations are represented by the functions of which the independent variable is only the strain size. Reference to a yield condition is not necessary. The friction coefficient of granular material is obtained automatically. Assuming Hooke's law in the elastic region, the modulus of elasticity E of glass bead granular material is 4.3 x 10(5) Pa; E of glass which is a matrix of glass beads is 7.5 x 10(10) Pa. These values roughly indicate the difference of mechanical characteristics between granular material and its matrix. The contribution of each term in the constitutive equations is large. Thus, 1-D stress strain relations are not able to extend to the usual 3-D stress-strain field. Simulation of real flow fields (the dynamics for the collapse of the granular layer and heap) using our constitutive relations by the smoothed particle hydrodynamics method and experimental verification are performed. Calculated results well describe details of the experimental collapse of the granular layer and the measured heap, including the early stage of collapse and the final heap formation. (c) Koninklijke Brill NV, Leiden and Society of Powder Technology, Japan, 2008.