Abstract: Based on the model of Southwell et al, we introduce two kinds of zonal wave -front reconstruction models in which subapertures are arranged in a geometry of equilateral triangle. The least-squares, the minimum norm solution, and the matrix iterative solution are given. The model analysis is carried out on the circular aperture rather than square aperture, which is often used by many researchers. Error propagation properties for the-two models are evaluated and compared with Southwell's model.