In this paper we explore parametric amplification on the Lamb wave acoustic platform for the purpose of developing nonlinear and non-reciprocal devices. The strength of the acoustic wave platform over the electromagnetic platform is its low loss and short wavelength at radio frequency which enables devices with a small footprint and high quality factor. Compared to surface acoustic waves, Lamb waves exhibit much higher phase velocity which support higher frequency operation with fabrication tolerance. To realize parametric amplification, the intrinsic nonlinear stiffness of aluminum nitride is used to couple acoustic waves at different frequencies. Novel Lamb wave resonator structures and non-reciprocal devices implementation have been proven in theory and simulation. Experiment of Lamb wave transducers demonstrates parametric effects and proves nonlinearity in AlN thin films.