Eleven double-mode (dm) RR Lyrae stars, with periods midway between the periods for the c-type and ab-type RR Lyrae stars, have been identified in the Draco dwarf galaxy by reanalyzing the photometry of Baade and Swope (1961) for 35 stars. The stars are V11, 72, 75, 83, 112, 138, 143, 156, 165, 169 and 190, three of which previously were noted as dm RR Lyraes by Goranskij (1982). The methods of Stellingwerf (1978) and Stobie (1970) were used to find the periods. The period ratios, periods and amplitudes suggest that the stars radially pulsate simultaneously in the fundamental and first overtone modes. The beat masses, estimated from the P1/P0 vs. P0 diagram (Petersen 1973), using as calibration the King Ia (Y=0.299, Z=0.001) models of Cox, Hodson and Clancy (1983, hereafter CHC), are Mbeat/Mo=0.65 for nine stars, = 0.60 for V75 and = 0.55 for V165. If the mass loss rate prior to arriving on the horizontal branch is proportional to the metal abundance (Stobie 1971, CHC), V75 and V165 should be more metal rich than the other nine dm RR Lyraes. In the period-amplitude (P-A) diagram, at a given amplitude, V165 has a smaller period shift relative to the standard M3 line than do the higher mass stars. Subsequently, the correlations of Preston (1959) and Sandage (1982) suggest that it is more metal-rich than the other nine dm RR Lyrae stars in Draco. Furthermore, reanalysis of the P-A and period-mean magnitude relations of all the RR Lyrae stars in Draco shows evidence for a widespread range in the metal abundances. Stars with large period shifts relative to the M3 relation are found to be more luminous than stars with smaller period shifts. The frequency of variable amplitude (ie. Blazhko effect) RR Lyrae stars is greatest for the ab-type stars with short periods. The brightnesses of the highest maxima appear to fit the P-A relation, and the amplitudes of the lowest maxima are variable, with V123 being an extreme example. Figure 3 of Szeidl (1975) shows the analogous situation for M3 RR Lyrae stars with the Blazhko effect. These findings suggest that the amplitude variability is related to the mode-switching activity of the dm RR Lyrae stars.