Four types of boundary conditions: Dirichlet, Neumann, transmitting, and modified transmitting, are derived by combining the damped wave equation with corresponding boundary conditions. The Dirichlet attenuating boundary condition is the easiest to implement. For an appropriate choice of attenuation parameter, it can achieve a boundary reflection coefficient of a few percent in a one-wavelength wide zone. The Neumann-attenuating boundary condition has characteristics similar to the Dirichlet attenuating boundary condition, but it is numerically more difficult to implement. Both the transmitting boundary condition and the modified transmitting boundary condition need an absorbing boundary condition at the termination of the attenuating region. The modified transmitting boundary condition is the most effective in the suppression of boundary reflections. For multidimensional modeling, there is no perfect absorbing boundary condition, and an approximate absorbing boundary condition is used.