Trilayer materials consisting of a functional outer layer on a substrate containing one intermediate layer are widely used in data-processing devices, biomedical components, and mechanical elements. The recent analytical frequency response functions (FRFs) derived by the authors' group for the contact of multilayer materials lead to the novel deterministic modeling of frictionless and frictional contact involving a trilayer material system designed with various thickness and elastic property combinations. Displacements and stresses for point contacts are calculated effectively by employing the discrete-convolution and fast Fourier transform (FFT) method based on the influence coefficients obtained from the analytical FRFs. The maximum von Mises stress and its location, which are critical information for understanding the material contact status, are thoroughly investigated for a wide range of trilayer materials. The results provide an informative guideline for the design of bilayer coatings without contact failure.