Synthetic Population of Interstellar Objects generates a synthetic population of interstellar objects (orbits and sizes) in arbitrary volume of space around the Sun. The only necessary assumption is that the population of ISOs in the interstellar space (far from any massive body) is homogeneous and isotropic. The assumed distribution of interstellar velocities of ISOs has to be provided as an input. This distribution can be defined analytically, but also in a discrete form. The algorithm, based on the multivariate inverse transform sampling method, is implemented in Python.