We show how Finite Model Computation (FMC) of first-order theories can efficiently and transparentlybe solved by taking advantage of an extension of Answer Set Programming, called incremental Answer Set Programming (iASP). The idea is to use the incremental parameter in iASP programs to account for the domain size of a model. The FMC problem is then successively addressed for increasing domain sizes until an answer set, representing a finite model of the original first-order theory, is found. We developed a system based on the iASP solver iClingo and demonstrate its competitiveness.