Choice of the correct distribution of sediment thicknesses is necessary in studying reflection of acoustic rays from randomly layered sediments and in many seismic applications. We consider a set of N segment lengths, {li}, i=1, 2, 3, ..., N, whose combined length is L. Three cases are of interest: 1) L and N are known constants, 2) the number of segments N is a known constant but L is a random variable with given expectation value , and 3) both N and L are random variables with given expectation values and , respectively. The distribution of segments lengths is calculated for each of the three cases under the assumption that any set {li} is as probable as any other set fulfiling the same conditions. The expressions are simple and easy to implement. ¿ American Geophysical Union 1988