We present numerical simulations of magnetoacoustic wave propagation from the photosphere to the low chromosphere in a magnetic sunspot-like structure. A thick flux tube, with dimensions typical of a small sunspot, is perturbed by a vertical or horizontal velocity pulse at the photospheric level. The type of mode generated by the pulse depends on the ratio between the sound speed cS and the Alfvén speed vA, on the magnetic field inclination at the location of the driver, and on the shape of the pulse in the horizontal direction. Mode conversion is observed to occur in the region in which both characteristic speeds have similar values. The fast (magnetic) mode in the region cS