Bacteriophage ϕX174 has been widely used as a model organism to study fundamental processes in molecular biology. However, several aspects of ϕX174 gene regulation are not fully resolved. Here we construct a computational model for ϕX174 and use the model to study gene regulation during the phage infection cycle. We estimate the relative strengths of transcription regulatory elements (promoters and terminators) by fitting the model to transcriptomics data. We show that the specific arrangement of a promoter followed immediately by a terminator, which occurs naturally in the ϕX174 genome, poses a parameter identifiability problem for the model, since the activity of one element can be partially compensated for by the other. We also simulate ϕX174 gene expression with two additional, putative transcription regulatory elements that have been proposed in prior studies. We find that the activities of these putative elements are estimated to be weak, and that variation in ϕX174 transcript abundances can be adequately explained without them. Overall, our work demonstrates that ϕX174 gene regulation is well described by the canonical set of promoters and terminators widely used in the literature.