Abstract: In order to solve the problems of non-uniformcross-section in the practice of deviation control, typtical mechanicalmodels of non-uniform stiffness are discussed in this paper. Based on thedifferential equations of deflection curve and conditions of continuity andboundary of non-uniform stiffness beam-column, the analytical calculationformulae for deflection and end slope angles of beam-column are derived.Furthermore, appling beam-column theory principle of superposition, themechanical problems of bottom hole assembly (BHA) with downhole control toolacted by a transverse concentrated force and BHA with variable gaugestabilizer can be solved. Non-uniform stiffness beam-column theory has beensuccessfully used in the mechanical analysis of BHA and it provides theoryfoundations for downhole control tool design, BHA optimization and deviationcontrol operation.