In this paper, we present and discuss results of two-dimensional simulations of linear and nonlinear magneto-acoustic wave propagation through an open magnetic flux tube embedded in the solar atmosphere expanding from the photosphere through to the transition region and into the low corona. Our aim is to model and analyze the response of such a magnetic structure to vertical and horizontal periodic motions originating in the photosphere. To carry out the simulations, we employed our MHD code SAC (Sheffield Advanced Code). A combination of the VALIIIC and McWhirter solar atmospheres and coronal density profiles were used as the background equilibrium model in the simulations. Vertical and horizontal harmonic sources, located at the footpoint region of the open magnetic flux tube, are incorporated in the calculations, to excite oscillations in the domain of interest. To perform the analysis we have constructed a series of time-distance diagrams of the vertical and perpendicular components of the velocity with respect to the magnetic field lines at each height of the computational domain. These time-distance diagrams are subject to spatio-temporal Fourier transforms allowing us to build ω-k dispersion diagrams for all of the simulated regions in the solar atmosphere. This approach makes it possible to compute the phase speeds of waves propagating throughout the various regions of the solar atmosphere model. We demonstrate the transformation of linear slow and fast magneto-acoustic wave modes into nonlinear ones, i.e., shock waves, and also show that magneto-acoustic waves with a range of frequencies efficiently leak through the transition region into the solar corona. It is found that the waves interact with the transition region and excite horizontally propagating surface waves along the transition region for both types of drivers. Finally, we estimate the phase speed of the oscillations in the solar corona and compare it with the phase speed derived from observations.