We consider the problem of bounded model checking for linear temporal logic with past operators (PLTL). PLTL is more attractive as a specification language than linear temporal logic without past operators (LTL) since many specifications are easier to express in PLTL . Although PLTL is not more expressive than LTL, it is exponentially more succinct. Our contribution is a new more efficient encoding of the bounded model checking problem for PLTL based on our previously presented encoding for LTL . The new encoding is linear in the bound. We have implemented the encoding in the NuSMV 2.1 model checking tool and compare it against the encoding in NuSMV by Benedetti and Cimatti. The experimental results show that our encoding performs significantly better than this previously used encoding.