When constructing a synthetic seismogram in the earthquake study or in seismic data interpretation by using a ray-tracing technique, the most troublesome and error-prone task is to define a suite of ray codes for the corresponding rays to trace in advance. An infinite number of rays exist for any arbitrarily located source and receiver in a medium. Missing certain important rays or an inappropriate selection of ray codes in tracing rays may result in wrong interpretation of the earthquake record or seismogram. Automatic ray code generation could be able to eliminate those problems. In this study we have developed an efficient algorithm with which one can generate systematically all the ray codes for the source(s) and receiver(s) arbitrarily located in a model. The result of this work could be used not only in analysing multiples in seismic data processing and interpretation, but also in coda wave study, study on the amplification effects in a basin and phase identification of the waves multiply reflected/refracted in earthquake study.