The increase in the advanced location based services such as traffic coordination and management necessitates the need for advanced models tracking the positions of Moving Objects (MOs) like vehicles. Computers cannot continuously update locations of MOs because of computational overhead, which limits the accuracy of evaluating MOs' positions. Due to the uncertain nature of such positions, efficiently managing and quantifying the uncertainty regions of MOs are needed in order to improve query response time. These regions can be rather irregular which makes them unsuitable for indexing. This paper presents Minimum Bounding Rectangles (MBR) approximations for three uncertainty region models, namely, the Cylinder Model ( ), the Funnel Model of Degree 1 ( ) and the Funnel Model of Degree 2 ( ). We also propose an estimation of the MBR of that achieves a good balance between computation time and selectivity (false-hits). Extensive experiments on both synthetic and real spatio-temporal datasets showed an order of magnitude improvement of the estimated model over the other modeling methods in terms of the number of MBRs retrieved during query process, which directly corresponds to the number of physical page accesses.