FOCUS (Fast Monte CarlO approach to Coherence of Undulator Sources) is a new GPU‐based simulation code to compute the transverse coherence of undulator radiation from ultra‐relativistic electrons. The core structure of the code, which is written in the language C++ accelerated with CUDA, combines an analytical description of the emitted electric fields and massively parallel computations on GPUs. The combination is rigorously justified by a statistical description of synchrotron radiation based on a Fourier optics approach. FOCUS is validated by direct comparison with multi‐electron Synchrotron Radiation Workshop (SRW) simulations, evidencing a reduction in computation times by up to five orders of magnitude on a consumer laptop. FOCUS is then applied to systematically study the transverse coherence in typical third‐ and fourth‐generation facilities, highlighting peculiar features of undulator sources close to the diffraction limit. FOCUS is aimed at fast evaluation of the transverse coherence of undulator radiation as a function of the electron beam parameters, to support and help prepare more advanced and detailed numerical simulations with traditional codes like SRW. FOCUS (Fast Monte CarlO approach to Coherence of Undulator Sources), a new GPU‐based code to compute the transverse coherence of X‐ray radiation from undulator sources as a function of the electron beam parameters, is described. FOCUS is validated with the Synchrotron Radiation Workshop (SRW) and SPECTRA codes. Examples of application to coherence studies in third‐ and fourth‐generation light sources are shown.