B^＋ -trees are considered standard organization for indexes in database systems. The concurrent control mechanism on B^＋ -trees has a great effect on the performance of DBMS supporting multi-users. A variant of B^＋ -tree called e-B^＋ -tree(elastic B^＋ -tree) is presented in this paper. Then, the safe nodes and operations on e--B^＋ trees are defined and the moment of reconstruction of e-B^＋tree is regulated. All these measures not only reduce the overhead for maintaining the e--B^＋ tree and the time spent on locking, but also decrease the frequency of splitting and catenating operation. Therefore, the degree of concurrency of operations on e-B^＋tree and efficiency of the database system can increase by a big margin.