A seven-port impedance and admittance matrices of multilayered piezoelectric beam are derived for the analysis of piezoelectric AFM ( atomic force microscope) cantilever that is partially covered by the piezoelectric layer. The variational principle is used for deriving the extensional and flexural motional equations and the conjugate parameters. Overall impedance matrix of AFM cantilever can be obtained by combining two impedance matrices of the covered and the non-covered. she resonance and antiresonance frequencies and the effective electromechanical coupling factors are calculated using the derived matrices. The results and the three dimensional finite element solutions are compared with the experimental results in other publication.