This　paper　presents　an　unconstrained　stress　updating　algorithm　for　a　critical　state　plastic　model　of　clay　soil,　where　the　loading/unloading　estimations　and　the　consideration　of　the　stress　behaviour　transition　from　elasticity　to　plasticity　can　be　bypassed　by　using　the　Fischer-Burmeister　smoothing　function　instead　of　the　Kuhn-Tucker　complementarity　conditions.　A　smoothing　tangent　operator　consistent　with　the　unconstrained　stress　updating　strategy　is　derived　from　preserving　the　quadratic　convergence　speed　for　the　global　solution.　Specifically,　the　relationship　and　difference　between　the　consistent　and　continuum　tangent　operators　are　analysed　from　the　perspectives　of　algebra　and　geometry.　In　addition,　the　nonlinear　constitutive　equations　obtained　by　the　backward　Euler　integration　scheme　are　solved　by　the　double　dogleg　trust　region　method　(improved　by　non　monotonic　technology),　where　a　larger　strain　increment　than　that　of　the　newton　method　is　allowed　for　the　stress　updating.　Then,　the　modified　Cam-clay　model　for　soil　is　implemented　in　ABAQUS/Standard　by　the　proposed　algorithm.　The　results　of　numerical　examples　show　that　the　algorithm　has　significant　advantages　in　terms　of　computation　efficiency　and　robustness　in　contrast　to　the　ABAQUS/Standard　default　integration　algorithm,　especially　for　the　condition　of　large　load　increments　and　cyclic　loadings.　More　than　twice　the　computational　efficiency　of　the　ABAQUS/Standard　default　integration　algorithm　can　be　observed　in　the　representative　numerical　examples.　The　source　code　of　the　proposed　algorithm　is　freely　available　at　https://git　hub.com/zhouxin615/NMTR_Method.　(c)　2021　Elsevier　B.V.　All　rights　reserved.