A class of multidimensional latent trait models is described. The properties of the model parameters, and initial results on the accuracy of a maximum likelihood procedure for estimating the model parameters are discussed. The model presented is a special case of the general model described by Rasch (1961), with close similarities to the models suggested by Bock and Aitkin (1981) and Samejima (1974). The concepts of item difficulty and discrimination were discussed in reference to this model as generalizations of the same concepts used in the unidimensional latent trait models. For this case, difficulty was shown to be defined by a function rather than a single value, and discrimination was shown to be related to the slope of the item characteristic surface at its intersection with the .5-plane. Both the difficulty function and discrimination parameters are most easily interpreted when determined conditional on a particular dimension. The maximum likelihood estimation procedure that was developed for the model was given an initial trial on a set of simulation data that was generated to contain two distinct dimensions. The item parameters estimated from the simulated test data were shown to be very highly related to the true parameters. (Author/PN)