The finite‐difference time‐domain (FDTD) approximation can be used to solve acoustical field problems numerically. Mainly because it is a time‐domain method, it has some specific advantages. The basic formulation of the FDTD method uses an analytical grid for the discretization of an unknown field. This is a major disadvantage. In this paper, FDTD equations that allow us to use a nonuniform grid are derived. With this grid, tilted and curved boundaries can be described more easily. This gives a better accuracy to CPU–resource ratio in a number of circumstances. The paper focuses on the new formulation and its accuracy. The problem of automatically generating the mesh in a general situation is not addressed. Simulations using quasi‐Cartesian grids are compared to Cartesian grid results.