Many applications of structural equation modeling involve ordinal (e.g., Likert) variables. A popular way of dealing with ordinal variables is to estimate the model with polychoric correlations rather than Pearson correlations. Such an estimation also requires the asymptotic covariance matrix of polychoric correlations. It is computationally intensive to estimate polychoric correlations and their asymptotic covariance matrices. We describe a computationally efficient R function PolychoricRM to estimate polychoric correlations and their asymptotic covariance matrix. The function invokes the computing power of modern Fortran and exploits multiple-core (multiple-thread) CPUs on nearly all current computers.