Abstract Numerical simulation has been widely used for predicting rock mass convergence during tunnel excavation. Considering that tunnel construction is a three-dimensional (3D) process, the 3D numerical analysis, instead of the plane-strain models, are commonly employed in engineering practice. As the 3D numerical analyses require large numbers of computational resources, the geometric extents are often kept to a minimum to reduce simulation time. However, there is a lack of published information concerning appropriate the size of numerical model. The study investigates how the transverse range of tunnel section, including the upper boundary, the lower boundary and the lateral boundary, affects the tunnel convergence via the finite difference software package FLAC3D, respectively. Then, a comprehensive function to yield the minimum transverse section area within a given error is proposed. After several cases with different categories of rock are employed in the simulations, the universal model extents with the minimum transverse section area are proposed.