The problem of reconstruction of vector and 2-tensor fields, given in refracting medium, is considered. The approach of direct reconstruction of a solenoidal part is presented. Least squares method is exploited for a reconstruction of solenoidal parts of original vector and 2-tensor fields by usage of certain solenoidal bases of polynomial type constructed for this purpose. The approach is justified theoretically by consideration of polynomial decompositions of polynomial vector and 2-tensor fields. The problems of existence, uniqueness and convergence of obtained approximation to the solenoidal part of original field are solved. The results of numerical simulation are presented and discussed.