NuRadioMC simulates ultra-high energy neutrino detectors that rely on the radio detection method, which exploits the radio emission generated in the electromagnetic component of a particle shower following a neutrino interaction. The code simulates the neutrino interaction in a medium, subsequent Askaryan radio emission, propagation of the radio signal to the detector and the detector response. NuRadioMC is a Monte Carlo framework that combines flexibility in detector design with user-friendliness. It includes an event generator, improved modeling of the radio emission, a revisited approach to signal propagation, and increased flexibility and precision in the detector simulation.