Acoustic waves, generated in solids by irradiation of a surface with powerful laser pulses, are widely used to study mechanical, thermal and elastic properties of materials. Application of this technique to MEMS technology will open new insights into fabrication and characterization but will require understanding of acoustic wave generation in small-sized objects. To that end, acoustic wave generation was studied in thin (10-50 μm) metal and semiconductor foils (including Mo, Si, W, Ni, Ta, Au) back-side irradiated by nanosecond IR and UV laser pulses over a range of peak intensities. Both interferometric techniques and capacitance transducers were employed for detection of surface displacements in the foils. By varying the peak laser power over a wide range of intensities (1-500 MW/cm2) detection of the transition from a thermoelastic to a laser-plasma driven shock-wave mechanism for acoustic wave generation was possible. Measurements show that this transition is accompanied by a dramatic change in the waveform of the generated shock-wave and that this waveform differs for various materials and foil thicknesses. Since thin foils were studied, the longitudinal and shear waves were experimentally indistinguishable, making the observed waveform very complex. Moreover, at higher peak laser powers, mechanical vibrations at resonance frequencies of the thin foils can occur and further complicate the analysis. Nevertheless, the observed phenomena can be described in the framework of a simplified theoretical model and can be used for materials testing in different applications.