A method of shearing interferometry for evaluating the basic statistical quantities of randomly flat and randomly rough curved surfaces of solids is presented. Using this method the root-mean-square (RMS) values of heights and slopes, the values of autocorrelation lengths, autocorrelation coefficients and one-dimensional height distribution functions of surface irregularities of these surfaces can be determined. The method can be utilized for characterizing the randomly rough surfaces of both transparent and opaque solids. The results of the statistical analysis obtained by this method for chosen samples of randomly rough surfaces agree very well with those achieved by means of a stylus-type surface instrument.