Many methods exist for reconstructing phylogenies from molecular sequence data, but few phylogenies are known and can be used to check their efficacy. Simulation remains the most important approach to testing the accuracy and robustness of phylogenetic inference methods. However, current simulation programs are limited, especially concerning realistic models for simulating insertions and deletions. We implement a portable and flexible application, named INDELible, for generating nucleotide, amino acid and codon sequence data by simulating insertions and deletions (indels) as well as substitutions. Indels are simulated under several models of indel-length distribution. The program implements a rich repertoire of substitution models, including the general unrestricted model and nonstationary nonhomogeneous models of nucleotide substitution, mixture, and partition models that account for heterogeneity among sites, and codon models that allow the nonsynonymous/synonymous substitution rate ratio to vary among sites and branches. With its many unique features, INDELible should be useful for evaluating the performance of many inference methods, including those for multiple sequence alignment, phylogenetic tree inference, and ancestral sequence, or genome reconstruction.