We introduce FD3D_TSN—an open‐source Fortran code for 3D dynamic earthquake rupture modeling based on the staggered grid fourth‐order finite‐difference method employing a regular cubical spatial discretization. Slip‐weakening and fast‐velocity‐weakening rate‐and‐state fault friction laws are combined with vertical planar fault geometry, orthogonal to a planar free surface. FD3D_TSN demonstrates good agreement with other methods in a range of benchmark exercises of the Southern California Earthquake Center and U.S. Geological Survey dynamic rupture code verification project. Efficient graphic processing units (GPU) acceleration using the OpenACC framework yields a factor of 10 speed‐up in terms of time to solution compared to a single‐core solution for current hardware (Intel i9‐9900K and Nvidia RTX 2070). The software is fast and easy‐to‐use and suitable explicitly for data‐driven applications requiring a large number of forward simulations such as dynamic source inversion or probabilistic ground‐motion modeling. The code is freely available for the scientific community and may be incorporated in physics‐based earthquake source imaging and seismic hazard assessment, or for teaching purposes.