Simple exact solutions have been tound for the modes of buckling or vibration of an equilateral triangular plate with supported edges. They may be classified as 1 (a)—modes symmetrical about all three medians, 1 (b)—modes symmetrical about one median, 2—modes anti-symmetrical about one median. Mode 2 obviously also covers the modes for a 60° right-angled triangle forming one half of the equilateral triangle. The frequency for each mode of type 2 duplicates that for a corresponding mode of type 1(b).