This paper presents efficient and easily implementable methods for the characteristic analysis and tolerance analysis of nonlinear resistive circuits using integer programming. In these methods, the problem of finding all characteristic curves or all solution sets (regions of possible operating points) is formulated as a mixed integer programming problem, and it is solved by a high-performance integer programming solver such as CPLEX. It is shown that the proposed methods can easily be implemented without making complicated programs, and that all characteristic curves or all solution sets are obtained by solving mixed integer programming problems several times. Numerical examples are given to confirm the effectiveness of the proposed methods.