Results of simulation studies evaluating the performance of statistical methods can have a major impact on the way empirical research is implemented. However, so far there is limited evidence of the replicability of simulation studies. Eight highly cited statistical simulation studies were selected, and their replicability was assessed by teams of replicators with formal training in quantitative methodology. The teams used information in the original publications to write simulation code with the aim of replicating the results. The primary outcome was to determine the feasibility of replicability based on reported information in the original publications and supplementary materials. Replicasility varied greatly: some original studies provided detailed information leading to almost perfect replication of results, whereas other studies did not provide enough information to implement any of the reported simulations. Factors facilitating replication included availability of code, detailed reporting or visualization of data-generating procedures and methods, and replicator expertise. Replicability of statistical simulation studies was mainly impeded by lack of information and sustainability of information sources. We encourage researchers publishing simulation studies to transparently report all relevant implementation details either in the research paper itself or in easily accessible supplementary material and to make their simulation code publicly available using permanent links.