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The abutment constraint problem is one of the common constraints in practice to favor the transmission of data between blocks. Based on corner block list (CBL), a new algorithm to deal with abutment constraints is developed in this paper. We can obtain the abutment information by scanning the intermediate solutions represented by CBL in linear time during the simulated annealing process and fix the CBL in case the constraints are violated. Based on this algorithm, a new method to deal with L-shaped/T-shaped blocks is proposed. The shape flexibility of the soft blocks and the rotation and reflection of L-shaped/T-shaped blocks are exploited to obtain a tight packing. The experimental results are demonstrated by some benchmark data and the performance shows the effectiveness of the proposed method.