Abstract Elastic optical networking has recently been proposed for use in optical transport networks to cope with increasingly heterogeneous and dynamic demand patterns. In this paper, we study the blocking performance of a multi-class elastic optical link for which a demand needs to be allocated a contiguous subset of the entire spectrum. This problem is different than the well-known blocking problem in multi-class multi-server loss systems due to the contiguous allocation constraint. We first propose a non-work-conserving aligned spectrum allocation policy which is shown to outperform the conventional first fit-based work-conserving allocation policy without alignment. Subsequently, for blocking performance of an aligned elastic optical link with up to three different traffic classes, we propose a novel and systematic order reduction procedure for MMPPs (Markov Modulated Poisson Process) and use this procedure as the numerical engine to approximately obtain the blocking probabilities. The proposed numerical algorithm is validated under various system and traffic parameters and is shown to be effectively usable as an instrument to dimension elastic optical links.