This manuscript is devoted to the development of methods for finding the diffusion coefficient of soil moisture and the thermal conductivity coefficient of soil by using the system of Lykov's equations for heat and mass transfer in the soil. The conjugate system of partial differential equations is constructed by using the direct initial-boundary value problem and additional boundary conditions on the accessible boundary of the region. Iterative formulas for finding the diffusion coefficient of soil moisture and the thermal conductivity coefficient are derived from the minimization of specially constructed functional and solution of direct and conjugate problems. The direct and conjugate problems are discretized by the Dufort-Frankel Difference scheme. An algorithm for solving the coefficient-inverse problem is developed and the program is designed in Matlab software package. Numerical calculations are conducted in order to verify the convergence of iterative processes.