A novel numerical technology based on finite-element methods has been developed for analyzing interaction problems in 1.5- and 2-D ultrasound arrays. A standard finite-element array model consists of structural elements encased in fluid. For accurate solutions, a portion of the fluid must be meshed and truncated with a radiation boundary condition which approximates an infinite domain. The essence of this new technology, termed overlapping grid, is that only the structural elements will actually be meshed. The surrounding air or water is automatically created as a uniform cubic mesh which is invisible to the user and properly connected to the structural mesh. In addition to obvious advantages for mesh creation, larger numerical models can be solved. For a hypothetical 3-D acoustic model where ten are structural and the rest fluid, the total storage required using the overlapping grid technology is one third of that required using the current finite-element storage techniques. The overlapping grid technology also results in a significant speedup in the most time-consuming part of an iterative solver algorithm, which is multiplication of a vector by the stiffness matrix.