The ideal forming theory[1], which has been developed as a direct design method, provides an optimization technique for forming processes undergoing plastic deformation. In the ideal flow, materials are prescribed to deform following the minimum plastic work path. Besides the general ideal forming theory[2,3], specific ideal forming theories for membrane sheet forming[4] as well as two-dimensional steady bulk forming[5-7] have been previously developed. In this work, the theory is extended for the non-steady bulk forming under the plane strain condition. In particular, kinematics to describe the deformation along the minimum plastic work path is successfully developed using the orthogonal convective coordinate system based on the characteristic method.