Many economically important characteristics of agricultural crops are measured as ordinal traits. Statistical analysis of the genetic basis of ordinal traits appears to be quite different from regular quantitative traits. The generalized linear model methodology implemented via the Newton-Raphson algorithm offers improved efficiency in the analysis of such data, but does not take full advantage of the extensive theory developed in the linear model arena. Instead, we develop a multivariate model for ordinal trait analysis and implement an EM algorithm for parameter estimation. We also propose a method for calculating the variance-covariance matrix of the estimated parameters. The EM equations turn out to be extremely similar to formulae seen in standard linear model analysis. Computer simulations are performed to validate the EM algorithm. A real data set is analyzed to demonstrate the application of the method. The advantages of the EM algorithm over other methods are addressed. Application of the method to QTL mapping for ordinal traits is demonstrated using a simulated baclcross (BC) population.