Algorithms and software for numerical modeling and inversion of electromagnetic logs in the wells drilled with biopolymer and oil-based mud are developed. The algorithms are based on linearized solutions of the forward and inverse problems of electromagnetic logging and permit fast modeling of induction logs and efficient recovery of electric conductivity around the well. Mathematical modeling is based on numerical-analytical solution of the 2D forward problem taking into account high conductivity contrast between the well and the formation. Linear inversion is based on SVD-decomposition of information matrix. The results of numerical modeling and inversion of synthetic and field logs at the intervals of fluid-saturated terrigenous and carbonate formations drilled using biopolymer and oil-based mud are given.