This work proposes a semi-elastic optimizationbased LiDAR-inertial state estimation method, which balances the constraints from LiDAR, IMU and consistency according to their unique characteristics, thereby imparts appropriate elasticity for current state to be optimized to the correct value, and ensure the accuracy, consistency, and robustness of state estimation. We incorporate the proposed LiDAR-inertial state estimation method into a self-developed optimizationbased LiDAR-inertial odometry (LIO) framework. Experimental results on four public datasets demonstrate that the proposed method enhances the performance of optimizationbased LiDAR-inertial state estimation. We have released the source code of this work for the development of the community.