The instability of a simple pin-supported beam when subject to a locally hydrostatic pressure distribution, the intensity of which is a function of distance along the beam only, is discussed in this paper. In particular, the pressure is assumed to follow a polynomial law given by Equation . The problem, basic assumptions, and precise definition of locally hydrostatic pressure are stated in the first section of the paper. The second section contains a discussion of the equations of equilibrium from which the basic differential equation is derived. The solutions of this differential equation satisfy the boundary conditions only for certain discrete values of the parameters involved, and these values in turn define the buckling loads. In the third section the buckling loads are tabulated for several cases in comparison with the buckling loads for the same beam subject only to an end thrust. The appendix contains a mathematical discussion of the solution of the basic differential equation and a derivation of the formula for the buckling loads.