My first thought was snapper but don't think so. The mower pictured is Similar [web search] but not it either, made for Montgomery Ward by ? It may be possible your mower is missing some sheet metal making it difficult to I.D. Any stamping on the frame?
That might be a Yardman brand built by the Yardman Mfg. Co.(not the MTD)? Having a B&S engine on it. Most of the Craftsmans I remember had Lauson/Tecumseh engines. Some with the windup starter.