We consider a special case of the n-component cubic model on the square lattice, for which an expansion exists in Ising-type graphs. We construct a transfer matrix and perform a finite-size-scaling analysis to determinethe critical points for several values of n. Furthermore we determine several universal quantities, includingthree critical exponents. For n﹤2, these results agree well with the theoretical predictions for the criticalO (n) branch. This model is also a special case of the (Nα, Nβ) model of Domany and Riedel. It appears that theself-dual plane of the latter model contains the exactly known critical points of the n=1 and 2 cubic models.For this reason we have checked whether this is also the case for 1﹤n﹤2. However, this possibility isexcluded by our numerical results.