Inversions are a common form of structural variation, which may have a marked effect on the genome and methods to infer quantities of interest such as those relating to population structure and natural selection. However, due to the challenge in detecting inversions, little is presently known about their impact. Software to simulate inversions could be used to provide a better understanding of how to detect and account for them, but while there are several software packages for simulating population genetic data, none incorporate inversion polymorphisms. Here, we describe a software package, modified from the forward-in-time simulator FREGENE, which simulates the evolution of an inversion polymorphism, of specified length, location, frequency and age, in a population of sequences. We describe previously unreported signatures of inversions in SNP data observed in invertFREGENE results and a known inversion in humans.