This paper deals with the problem of estimating the parameters of the Rice distribution. The distribution has applications in sonar and radar signal processing and a proper estimation procedure with associated confidence intervals is important. Using the sample second moment as an estimate of the second moment of the distribution, two techniques, viz., methods of moments and maximum likelihood are applied to synthetic envelope data of known signal-to-noise ratios, in order to estimate the parameter from different sample sizes. It is concluded that the sample second moment is an unbiased estimate of the theoretical second moment and for the signal-to-noise ratio parameter both methods work without any significant bias and satisfy the criterion of maximum efficiency. However, the method of moments is simpler, easier to apply and therefore recommended as the method of choice.