This paper focuses on real-time tracking of an extended object in the presence of clutter. This task reduces to the estimation of the object kinematic state and its extent, based on multiple measurements originated from the same object. A solution to this challenging problem is presented within the recently proposed Box Particle Filtering framework. The Box Particle Filter replaces the point samples with regions, which we call boxes. The performance of the Box Particle Filter for extended object tracking is studied over a challenging scenario with simulated cluttered radar measurements, consisting of range and bearing components. The efficiency is evaluated for different levels of clutter, number of box particles, uncertainty regions for the measurements, number of the active sensors collecting the measurements data and iterations for the contraction of the uncertainty region. Accurate estimation results are demonstrated.