This paper mainly discusses some effective domain decomposition preconditioners for static elastic crack problems modeled by geometrical extended finite element method. To construct the Schwarz type preconditioners, we adopt a special crack-tip domain decomposition strategy. The finite element mesh is decomposed into "crack tip" subdomains, which contain all the degrees of freedom (DOFs) of the branch enrichment functions, and "regular" subdomains, which contain the standard DOFs and the DOFs of the Heaviside enrichment functions. Based on the crack-tip domain decomposition strategy, an effective class of multiplicative and restrict multiplicative Schwarz preconditioners are derived. In the preconditioners, the crack tip subproblems are solved exactly and the regular subproblems are solved by some inexact solvers. Numerical experiments demonstrate the effectiveness of the preconditioners.