Many large-scale assessments are designed to yield two or more scores for an individual by administering multiple sections measuring different but related skills. Multidimensional tests, or more specifically, simple structured tests, such as these rely on multiple multiple-choice and/or constructed responses sections of items to generate multiple scores. In the current article, we propose an extension of the hierarchical rater model (HRM) to be applied with simple structured tests with constructed response items. In addition to modeling the appropriate trait structure, the multidimensional HRM (M-HRM) presented here also accounts for rater severity bias and rater variability or inconsistency. We introduce the model formulation, test parameter recovery with a focus on latent traits, and compare the M-HRM to other scoring approaches (unidimensional HRMs and a traditional multidimensional item response theory model) using simulated and empirical data. Results show more precise scores under the M-HRM, with a major improvement in scores when incorporating rater effects versus ignoring them in the traditional multidimensional item response theory model.