Methods for sealing undesirable transverse fractures enlarged and/or created during lithological displacement of an underground water-soluble evaporite stratum by hydraulic pressure greater than overburden pressure at an evaporite/non-evaporite strata interface, comprising injecting and maintaining a sealing agent into these undesirable fractures to form a solidified matter in situ and ultimately seal them, while forming a main free surface at the interface suitable for initiating solution mining of the evaporite stratum. The solidified matter may be crystallized, precipitated, compacted, agglomerated, cross-linked, coagulated, water-swollen, and/or cemented matter, or may include a wall-building matter with the mineral on fracture faces. The sealing agent may comprise at least one component of the mineral and/or the non-evaporite. The evaporite stratum is preferably a trona stratum overlying an oil shale stratum. The sealing agent may comprise dissolved and/or solid trona, trona tailings particles, and/or water-swelling particles.