in this talk, first i will present a kernel-free boundary integral (kfbi) method for the linearized poisson-boltzmann equation, which may have variable coefficients and is in general not applicable for the standard boundary integral method. then i will present the kfbi method for the nonlinear poisson-boltzmann equation. the kfbi method is a cartesian grid method. it uses cartesian grid-based solutions to compute approximations to boundary and volume integrals involved in the solution of boundary integral equations for the poisson-boltzmann equation. i will also present numerical examples in both two and three space dimensions to demonstrate the efficiency and accuracy of the kfbi method.