In order to better understand complex diseases, it is important to understand how genetic variation in the regulatory regions affects gene expression. Genetic variants found in these regulatory regions have been shown to activate transcription in a tissue-specific manner. Therefore, it is important to map the aforementioned expression quantitative trait loci (eQTL) using a statistically disciplined approach that jointly models all the tissues and makes use of all the information available to maximize the power of eQTL mapping. In this context, we are proposing a score test-based approach where we model tissue-specificity as a random effect and investigate an overall shift in the gene expression combined with tissue-specific effects due to genetic variants.