Based on the classic 2D strike-slip fault model by Savage & Burford (1973), we propose the 2D extended strike-slip fault segment model with both locking and creeping in the interseismic period. First, we give the definition of the fault with locking and creeping (Lc fault / Lc model); then, the model which meets the definition of the Lc fault is constructed and the results of the Lc model are numerically simulated which is the same as that of SB73 model except for a scale factor. We further prove the correctness of the results mathematically and give the model of the couple fraction by Lc model. The results of Lc model illustrate that the not one-to-one correspondence between surface deformation and fault mechanism could be more complicated.