This paper presents a set of comprehensive and accurate results for the free-flexural vibration of triangular plates of arbitrary boundary conditions with/without curved internal supports. These results are presented for ten distinct cases involving the combinations of free, simply supported or clamped edge conditions. In the present study, a simple and straightforward pb-2 Rayleigh-Ritz method is employed to determine the first few natural frequencies for the triangular plates with a wide range of aspect ratios; i.e., (a / b=2 / 5,1 /) (2,1,2 / \sqrt{3}) and 2. A set of pb-2 Ritz functions consisting of the product of a two-dimensional polynomial function and a basic function is used. The basic function is defined by the product of (1) equations of the prescribed continuous piecewise boundary each raised to the power of 0,1 or 2 , corresponding to a free, simply supported or clamped edge, and (2) equations of the internal supports. The members of the generated set of functions satisfy automaticaly all the kinematic boundary conditions of the plate at the outset. The present results for some cases are compared with available published values from the open literature.