This paper investigates the particular problem of matrices appearing during the modeling of Integrated Circuits with Finite Integration Technique (FIT) method. We present the key points of FIT approach followed by an illustration of the structure and the properties of the FIT-type matrix. A novel algorithm SMark is proposed, which focuses on fill-ins number reduction. The main idea of SMark is the concept of a dual architecture—symbolic and numeric factorization. In order to validate SMark a comparison with other methods was performed. The excellent results confirm that the proposed approach is an adequate solving method for FIT-type matrices, whereas the identified weak points of the algorithm indicate possible directions in the future work.