Abstract: Pre-aggregation is one of the most effective techniques in OLAP to ensure quick responses to user queries in data warehouses. The technique usually requires dimension hierarchies to be onto, covering and self-onto. However, in real-world applications, many irregular dimensions do not meet the requirements. To solve the problem, a novel dimension model is proposed to support the modeling of irregular dimensions by defining a partial mapping from a child level to a parent level. Based on the four cases of the partial mappings among different levels, the model can express the special relationships among the levels in irregular dimensions, such as non-covering and non-onto relationships. Furthermore, a cube model is defined based on the dimension model, along with some typical OLAP operations. The mapping from the multidimensional model to relational tables shows that the model provides a feasible way to overcome the difficulties caused by irregular dimensions.