An approximate method of stress analysis in elastic solids with multiple cracks is proposed to improve the accuracy of the Kachanov method in analyzing closely spaced cracks. Classical Kachanov method assumed that traction in each crack can be represented as the sum of a uniform component and a nonuniform one, and that the interaction among the cracks is only due to the uniform components. The assumptions simplify considerably the mathematics. However, they may not be valid when the cracks are very close and overlap along the direction of load, because each crack may be embedded in the stress-amplifying region as well as the stress-shielding region of the other cracks at this time. To improve the accuracy of the Kachanov method, a new asymptotic method, in which the influence on a crack of the quadratic parabola pseudotractions (QPPTs) rather than the average ones on the other crack are taken into account, is proposed. Applications to the problem of three collinear cracks and two offset parallel closely spaced cracks are considered to validate the accuracy of the new method.