This chapter discusses free vibration of triangular plates in the most general form, viz., for triangular domain of arbitrary shape and size and with all possible types of boundary conditions on the three edges. Various researchers around the globe have studied free vibration of triangular plates. The work of Leissa, being an excellent monograph, has information related to triangular plates. The methods in those investigations range from experimental to approximate by employing a few term approximations with Rayleigh–Ritz or collocation methods. In some cases, the finite difference methods were also employed. Rayleigh–Ritz method with boundary characteristics orthogonal polynomials as the basis functions is applied to generate a sequence of approximations. The process is terminated when the required number of frequencies is converged to the desired accuracy.