We propose an extension of standard methods for computing pedigree likelihoods, in which pedigree founders are allowed to be inbred. Support for inbred founders is implemented in the forrel R package for forensic pedigree analysis. This enables for the first time background inbreeding to be modelled and studied in a variety of applications, including likelihood ratios, exclusion probabilities, relatedness inference and simulation studies. We illustrate these advances through two study cases.