The numerical solution of the two‐dimensional (2‐D) acoustic equations as a hyperbolic system by the use of the finite‐difference method has been investigated. For efficient computation, the numerical domain must be truncated by an absorbing boundary condition. Deriving nearly reflectionless conditions that are both accurate and stable for spherical waves is nontrivial. In this paper, absorbing boundary conditions are developed for the case of an acoustic pulse radiated from a spherical monopole source. Numerical results are presented comparing conditions based on a characteristic variable formulation to conditions based on the Bayliss–TurkelB1condition. It was found that the best conditions were those employing the Bayliss–TurkelB1condition on the acoustic density deviation (or equivalently the acoustic pressure) and a particular condition on the particle velocity component normal to the absorbing boundary.