The paper presents a multifrontal method for solving indefinite sparse symmetric linear systems. The method extends the frontal method to allow multiple fronts to occur simultaneously, enabling the solution of general symmetric systems. The approach uses the minimum-degree ordering to select pivots and ensures numerical stability. The algorithm is divided into three phases: ANALYZE, FACTOR, and SOLVE. The ANALYZE phase determines the sparsity pattern and pivot order, the FACTOR phase performs numerical factorization, and the SOLVE phase solves the system. The method is tested on both scalar and vector machines, showing improved performance on vector machines due to vectorization of inner loops. The algorithm is efficient and robust, handling indefinite systems by using a mixture of 1×1 and 2×2 pivots. The paper also discusses the use of assembly trees and the benefits of minimum-degree ordering in reducing storage and computation time. The results show that the method is competitive with existing codes and provides significant speed improvements on vector machines. The approach is applicable to a wide range of sparse symmetric systems and is efficient in both storage and computation.The paper presents a multifrontal method for solving indefinite sparse symmetric linear systems. The method extends the frontal method to allow multiple fronts to occur simultaneously, enabling the solution of general symmetric systems. The approach uses the minimum-degree ordering to select pivots and ensures numerical stability. The algorithm is divided into three phases: ANALYZE, FACTOR, and SOLVE. The ANALYZE phase determines the sparsity pattern and pivot order, the FACTOR phase performs numerical factorization, and the SOLVE phase solves the system. The method is tested on both scalar and vector machines, showing improved performance on vector machines due to vectorization of inner loops. The algorithm is efficient and robust, handling indefinite systems by using a mixture of 1×1 and 2×2 pivots. The paper also discusses the use of assembly trees and the benefits of minimum-degree ordering in reducing storage and computation time. The results show that the method is competitive with existing codes and provides significant speed improvements on vector machines. The approach is applicable to a wide range of sparse symmetric systems and is efficient in both storage and computation.