The paper describes a method for calculating the longitudinal and transverse impedances of the laminated round pipe with many layers of different materials. The charge is moving along the pipe axis with arbitrary constant velocity. The study is based on the field-matching technique applied for the arbitrary harmonic of the electromagnetic field. The matrix formalism has been developed to describe the field transitions through the subsequent layers that allow coupling the electromagnetic fields inside and outside the pipe. The number of equations to be solved is then reduced to four algebraic equations. The solutions and ultrarelativistic limits for the field harmonics in the inner and outer regions of the pipe are derived.