A general three-dimensional concurrent multiscale modeling approach is developed for amorphous materials. The material is first constructed as a tessellation of hexahedral amorphous cells. For regions of linear deformation, the number of degrees of freedom is reduced by computing the displacements of the vertices of the amorphous cells only instead of the atoms within. This is achieved by determining, a priori, the atom displacements within such pseudoamorphous cells associated with orthogonal deformation modes of the cell. Actual atom displacements are calculated using traditional molecular mechanics for regions of nonlinear deformation. Computational implementation of the coupling between pseudoamorphous cells and molecular mechanics regions and stiffness matrix formulation are elucidated. Multiscale simulations of nanoindentation on polymer and crystalline substrates show good agreement with pure molecular mechanics simulations. Copyright © 2012 John Wiley & Sons, Ltd.