For the mutiturn and multilayer solenoid with finite rectangular dimension，it is very difficult to obtain the analytical formula for the axial magnetic field distribution. Based on the analytical formulae for the single turn rectangular wire and that for the multitun and single layer rectangular solenoid，the sum expression of the axial magnetic field distribution for the the mutiturn and multilayer solenoid is obtained. A Matlab script is written based on the slice and sum method proposed in this paper. Finally，an analysis on the axial magnetic field distribution for a beam orbit corrector most applied at the low energy stage of the accelerators is done. The result calculated by the Matlab script and the numerical simulation result by CST EM studio agree well