Bivariate clustered (correlated) data often encountered in epidemiological and clinical research are routinely analyzed uneer a linear mixed model (LMM) framework with underlying normality assumptions of the random effects and within-subject errors. However, such normality assumptions might be questionable if the data set particularly exhibits skewness and heavy tails. Using a Bayesian paradigm, we use the skew-normal/independent (SNI) distribution as a tool for modeling clustered data with bivariate non-normal responses in an LMM framework.