Digital tomosynthesis is a three-dimensional imaging technique with a lower radiation dose than computed tomography (CT). Due to the missing data in tomosynthesis systems, out-ofplane structures in the depth direction cannot be completely removed by the reconstruction algorithms. In this work, we analyzed the impulse responses of common tomosynthesis systems on a plane-to-plane basis and proposed a fast and accurate convolution-based blur-and-add (BAA) model to simulate the backprojected images. In addition, the analysis formalism describing the impulse response of out-of-plane structures can be generalized to both rotating and parallel gantries. We implemented a ray tracing forward projection and backprojection (ray-based model) algorithm and the convolution-based BAA model to simulate the shift-and-add (backproject) tomosynthesis reconstructions. The convolution-based BAA model with proper geometry distortion correction provides reasonably accurate estimates of the tomosynthesis reconstruction. A numerical comparison indicates that the simulated images using the two models differ by less than 6% in terms of the root-mean-squared error. This convolution-based BAA model can be used in efficient system geometry analysis, reconstruction algorithm design, out-of-plane artifacts suppression, and CT-tomosynthesis registration.