Self-pierce riveting (SPR) is nowadays widely used in the car manufacturing industry where aluminium alloys are used for body construction. For the design of mechanical structures, formed by the joining of component parts, a knowledge of the vibration characteristics of different joint types (adhesive bonding, spot welding, SPR etc) is essential. The free transverse vibration characteristics of single lap-jointed encastre SPR beams are investigated theoretically in this paper using the three dimensional finite element method (FEM). Numerical examples are provided to show the influence on the natural frequencies, natural frequency ratios and mode shapes of these beams caused by variations in the material properties (E and υ) of the sheet material. It is shown that the transverse natural frequencies of single lap jointed encastre SPR beams increases significantly as the Young’s Modulus of the sheets increases, but only slight changes are encountered for variations of Poisson’s Ratio. It is found that an exponential curve gives an acceptable fit to the relationship between natural frequency and Young’s Modulus. As expected, odd modes shapes were found to be symmetrical about the mid-length position and even modes were anti-symmetrical.