The stress intensity of three-dimensional corner singularity is computed for the tip of a transverse crack terminating on the free surface in a laminated composite. Firstly, stress singularity is calculated via finite element method applied for the angular domain. Then the two-state M-integral is employed, in conjunction with eigenfunction expansion, for computing the stress intensity of the stress singularity. The numerical example demonstrates the effectiveness of the proposed computational scheme. (c) 2005 Elsevier Ltd. All rights reserved.