Elliptic boundary-value problems can be reduced to integral equations on the boundary by many different ways. The canonical reduction, suggested by Prof. Feng Kang, is a natural and direct approach of boundary reduction. This paper gives the numerical method for solving harmonic and biharmonic canonical integral equations in interior or exterior circular domains, together with their convergence and error estimates. Using the theory of distributions, the difficulty caused by the singularities of integral kernel is overcome. Results of several numerical calculations verify the theoretical estimates.