Bandwidth variable-wavelength cross connect switches (BV-WXCs) play an important role in the routing and spectrum assignment (RSA) problem in elastic optical networks (EONs). These switches, whose structure has been derived from micro electro mechanical systems technology, aim to switch the incoming traffic flexibly such that the existing resources are not wasted and more requests can be served. There exist different quality of service parameters which have to be provided in EON, such as delay, loss, jitter, and so forth. Among these parameters, blocking probability (BP) has been always taken into account in EON and several researches have been done to address it. The main objective of most RSA algorithms is to alleviate BP of requests through efficient usage of resources, such as frequency slots and BV-WXC ports. To show the importance of BV-WXC in routing and resource assignment in EON, its performance is analyzed in this paper. The BP of the BV-WXC is evaluated by means of an analytical model under unicast traffic and the obtained results are compared to the blocking probability results acquired from simulations for different number of input/output ports and available resources. The obtained results show that the analytical model has a good agreement with the simulation results.