Spatial seemingly unrelated regression (spatial SUR) models are a useful multiequational econometric specification to simultaneously incorporate spatial effects and correlated error terms across equations. The purpose of the spsur R package is to supply a complete set of functions to test for spatial structures in the residual of a SUR model; to estimate the most popular specifications by applying different methods and test for linear restrictions on the parameters. The package also facilitates the estimation of socalled spatial impacts, conveniently adapted to a SUR framework. The package includes functions to simulate datasets with the features decided by the user, which may be useful in teaching activities or in more general research projects. The article concludes with a real data application showing the potential that spsur has to examine the relation of individual mobility over geographic areas and the incidence of COVID-19 in Spain during the first lockdown.