In studies of the source mechanism of small intraplate earthquakes the analysis of surface wave spectra is extremely valuable because reliable P wave solutions of these earthquakes are difficult to obtain. To determine the source mechanism using surface waves alone, phase and amplitude spectra must be analyzed. In this study of the southeastern Missouri earthquake of October 21, 1965, we examine the phase spectra of Rayleigh waves over periods of 20--50 s to follow up Mitchell's (1973) analysis of spectral amplitudes. It is shown that using known regionalized dispersion curves to remove propagation effects, we can isolate focal phase spectra and determine the mechanism of the earthquake. The results provide conclusive evidence for normal faulting with a NNW-SSE axis of tension. Thus our analysis of phase spectra gives results which are complementary as well as supportive to those obtained by Mitchell (1973).