American Dollar (USD) and Indian Rupee (INR) play an important role in Mauritian economy. It is important to model the pattern of dependence in their co-movement with respect to Mauritian Rupee (MUR), as this may indicate the export-import behavior in Mauritius. However, it is known that distributions of exchange rates are usually non-normal and the use of linear correlation as a dependence measure is inappropriate. Moreover it is quite difficult to obtain the joint distribution of such random variables in order to specify the complete covariance matrix to measure their dependence structure. In this paper, we first identify the marginal distributions of the exchange rates of MUR against USD and INR and then select the best fitting copula model for the bivariate series. It is concluded that both the series are asymmetric and fat-tailed following hyperbolic distribution. Their dependence structure is appropriately modeled by t copula.