Supernova 1993J (SN 1993J) in M81, now classified as Type IIb, is a strongly emitting radio supernova whose size can be resolved and whose growth can be monitored with the technique of very long baseline interferometry (VLBI). The results could provide important information about the circumstellar matter and the degree of asymmetry of the explosion. For several models of the emission of the radio supernova, we report estimates of its angular sizes 29 and 36 days after explosion at the wavelengths of 3.6 and 1.3 cm, respectively. These results, which correspond to our first epochs in an ongoing effort to determine the super-nova structure and its growth, slightly favor an optically thick uniform disk model, given the recently derived Cepheid distance to M81 and the estimated maximum supernova expansion speed. Further VLBI observations, combined with the expansion-speed data, may yield an independent estimate of the distance to M81.