A multidimensional item response theory (IRT) model for polytomously scored items, based on the graded response model and using the normal ogive, is developed; and an EM algorithm that may be used to estimate the parameters of the model is also discussed. The model is illustrated through a simulation study in which the polytomous item responses of 6 items and 5,000 respondents were generated by the RESGEN computer program. The relationships between the factor loadings and multidimensional parameters like those of the model of M. D. Reckase (1985) are established. The multidimensional parameters provide useful interpretations of parameters of the multidimensional item response models that can be computed directly from the factor loadings. Estimating the parameters of the multidimensional graded response model is a first step in expanding the application of factor analysis to qualitative data. Four tables and nine computer-generated graphical plots illustrate the analysis. (SLD)