A new unified axisymmetric characteristics line theory for weight materials is proposed based on the twin shear failure criterion; and pressures acting on the shaft wall are researched; and a new calculating method is given out with the new axisymmetric characteristics line theory. Example results show that the relationship between the pressures and the shaft depth is nonlinear. The parameter b in the twin shear unified strength criterion has significant effect on pressures. The larger the b is

the less the pressures are when shaft is at the same depth.