Materials science is one of the most important research areas. The wave phenomena in materials science are explained by the dynamics of nonlinear lattices that are generally considered by one-dimensional monatomic chains. The generalisation of monatomic lattices is the well-known diatomic theory, which is used to model the energy transport and the dynamics of real materials. The diatomic models have nonlinear strain waves which depend on both elasticity and width of the lamina. This is represented by balancing nonlinearity and dispersion terms and additionally, a direct continuum approach was developed to account for the behaviour of diatomic materials. In this work, wave solutions of the diatomic models are obtained via ansatz-based methods. The results can be used to improve new processes or applied to new areas.