Experiments dealing with laser mode structure are presented which are suitable for an upper division undergraduate laboratory. The theory of cavity modes is summarized. The mode structure of the radiation from a helium-neon laser is measured by using a photodiode detector and spectrum analyzer to detect intermode beating. Off-axial modes can be visually detected in the expanded laser beam and their presence correlated with signals displayed on the spectrum analyzer in agreement with the theory. (Author/TS)