Abstract The standard models for genomic prediction assume additive polygenic marker effects. For epistatic models including marker interaction effects, the number of effects to be fitted becomes large, which require computational tools tailored specifically for such models. Here, we extend the methods implemented in the R package bigRR so that marker interaction effects can be computed. Simulation results based on marker data from Arabidopsis thaliana show that the inclusion of interaction effects between markers can give a small but significant improvement in genomic predictions. The methods were implemented in the R package EPISbigRR available in the bigRR project on R-Forge. The package includes an introductory vignette to the functions available in EPISbigRR.