Résumé : One of the most widely used technique to obtain transient measures is the uniformization method. However, although uniformization have many advantages, the computational cost required to calculate transient probabilities are very large for stiff models. We study efficient solutions that can be applied to an approximate method developed for calculating transient state probabilities of Markov models, and cumulative expected reward measures over a finite interval. The method our work is based on, approximates the state probabilities at time t by the state probabilities calculated at a random time with Erlangian distribution. The original method requires an inversion of a matrix obtained from the state transition rate matrix, which destroys special structures such as sparseness and banded matrices. This precludes the use of the technique for large models. In our work we propose efficient solutions that can take advantage of special structures. Finally, we present examples which show that the proposed technique is computationally very efficient for stiff models when compared with uniformization.