We present the R package mixsmsn, which implements routines for maximum likelihood estimation (via an expectation maximization EM-type algorithm) in finite mixture models with components belonging to the class of scale mixtures of the skew-normal distribution, which we call the FMSMSN models. Both univariate and multivariate responses are considered. It is possible to fix the number of components of the mixture to be fitted, but there exists an option that transfers this responsibility to an automated procedure, through the analysis of several models choice criteria. Plotting routines to generate histograms, plug-in densities and contour plots using the fitted models output are also available. The precision of the EM estimates can be evaluated through their estimated standard deviations, which can be obtained by the provision of an approximation of the associated information matrix for each particular model in the FMSMSN family. A function to generate artificial samples from several elements of the family is also supplied. Finally, two real data sets are analyzed in order to show the usefulness of the package.5412120