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A system of coupled differential equations relates the amplitudes of alpha particle waves emitted from a spheroidal nucleus described by the Bohr–Mottelson model. These equations in spheroidal coordinates have been solved for five even–even nuclides with the aid of the electronic computer FERUT. There are four possible cases for each nuclide which are consistent with the boundary conditions. The solutions of the equations are used to calculate the probability density of alpha particles on the nuclear surface for each case. For Case I the peak in the distribution function shifts from the nuclear symmetry axis to the equator with increasing mass number. The probability density for Case II is always peaked between the symmetry axis and the equator, while for Cases III and IV it is always peaked strongly at the equator. The change in the distribution function with increasing distance from the nucleus is considered for a typical case. Barrier penetration factors are calculated and found to differ from those for spherical nuclei by factors of the order of 2 or 3. Comparison with the calculations of an approximation method of Fröman is made for one nuclide.