We present moes, a ray tracing software package that computes the path of rays through echelle spectrographs. Our algorithm is based on sequential direct tracing with Seidel aberration corrections applied at the detector plane. As a test case, we model the CARMENES VIS spectrograph. After subtracting the best model from the data, the residuals yield an rms of 0.024 pix, setting a new standard for the precision of the wavelength solution of state-of-the-art radial velocity (RV) instruments. By including the influence of the changes of the environment in ray propagation, we are able to predict instrumental RV systematics at the 1 m/s level.