This paper defines a constraint-based model dedicated to multidimensional databases. The model we define represents data through a constellation of facts (subjects of analyse) associated to dimensions (axis of analyse), which are possibly shared. Each dimension is organised according to several hierarchies (views of analyse) integrating several levels of data granularity. In order to insure data consistency, we introduce 5 semantic constraints (exclusion, inclusion, partition, simultaneity, totality) which can be intra-dimension or inter-dimensions; the intra-dimension constraints allow the expression of constraints between hierarchies within a same dimension whereas the inter-dimensions constraints focus on hierarchies of distinct dimensions. We also study repercussions of these constraints on multidimensional manipulations and we provide extensions of the multidimensional operators.