We design a class of accurate and efficient absorbing boundary conditions for molecular dynamics simulations of crystalline solids. In one space dimension, the proposed matching boundary conditions take the form of a linear constraint of displacement and velocity at atoms near the boundary, where the coefficients are determined by matching the dispersion relation with a minimal number of atoms involved. Bearing the nice features of compactness, locality, and high efficiency, the matching boundary conditions are then extended to treat the out-of-plane wave problems in the square lattice. We construct multidirectional absorbing boundary conditions via operator multiplications. Reflection coefficient analysis and numerical studies verify their effectiveness for spurious reflection suppression in all directions. Compact and local in both space and time, they are directly applicable to nonlinear lattices and multiscale simulations. Copyright © 2012 John Wiley & Sons, Ltd.