In the recent year, social networks have revolutionized the ways of interacting and exchanging information on the Internet. Millions of users interact frequently and share variety of digital content with each other. They express their feelings and opinions on every topic of interest. These opinions carry import value for personal, academic, and commercial applications, but the volume and the speed at which these are produced make it a challenging task for researchers and the underlying technologies to provide useful insights into such data. We attempt to extend the established online analytical processing (OLAP) technology to allow multidimensional analysis of social media data. In this paper, we pursue a goal of providing a generic multidimensional model dedicated to the OLAP of social media and specially Twitter. The proposed model reflects on some specifics such as recursive references between tweets, Empty dimension, and different types of hierarchies. It is implemented using NetBeans IDE platform. We present also some experimental results. We expect our proposed approach to be applicable for analyzing the data of other social networks as well.