This paper presents an analysis of the blocking phenomenon in circuit-switched routing policies with alternate routing and trunk reservation. From the usual assumptions on the offered traffic (Poisson) and the service time (exponential distribution), a classical Markov chain model is derived. Some approximate formulas are given to compute the blocking probabilities for first- and second-choice traffic. The accuracy of the proposed estimates is evaluated by direct comparison with already known results in simple cases and with the exact solution of the state equations.