Multi-lateral well drilling is the extension and development of horizontal well drilling and an effective tool for improvement of oil and gas recovery and economics. It is widely applied in oil and natural gas exploitation, but rarely in soluble mineral production. In this paper, the application of the technique in trona mining is introduced in the case of H032 well drilling at the Kazan Trona Mine. With the help of directional drilling technique, two parallel horizontal laterals were drilled from one main well bore to connect two pairs of vertical wells respectively to form 2 mining passages. The difficulties in applying the technique in the trona mine projectis analyzed with focus on the multi-lateral drilling process, such as well structure design and optimization, suspended sidetrack drilling, drill bit and BHA design and optimization, drilling fluid design, etc.