Abstract: In this paper, the kinematically admissible velocity field with surface crack on forward extruding bar is put forward during the axisymmetric cup-bar combined extrusion process, in accordance with the results of model experiments.On the basis of velocity field, the necessary condition for surface crack formation on the forward extruding bar is derived, with the help of upper bound theorem and the minimum energy principle. Meanwhile, the relationships between surface crack formation and combination of reduction in area for the part of forward and backward extursions (ε_b,ε_f) relative residual thickness of billet (T/R₀),frictional factor (m) or relative land length of ram and chamber (l_b|R₀,l_f|R₀) are calculated during the extrusion process. Therefore, whether the surface crack on forward exturding bar occurs can be predicted before extruding the lower-plasticity metals for axisymmetric cup-bar combined extrusion process.The analytical results agree very well with experimental results of aluminium alloy LY12 (ASTM 2024) and LC4 (ASTM 7075).