An analysis of known analytical and numerical weight functions for cracks in mode I has revealed that they all have a similar singular term and that it is possible to approximate them with one universal expression with three unknown parameters. The unknown parameters can be determined directly from reference stress intensity factor expressions without using the crack opening displacement function. The universal weight function expression, with suitable reference stress intensity factors, was used to derive the weight functions for internal and external radial cracks in a thick cylinder. These weight functions were then further used to calculate the stress intensity factors for radial cracks in a cylinder subjected to several nonlinear stress fields and were compared to available numerical data. NOMENCLATURE P(X) S, %(X7 a) X dx) a19 %(X),%(X), a,,(x) fJ0 K crack length modulus of elasticity geometric correction factor for the reference stress intensity factor K,, K,, , or K,z geometric stress intensity correction factor for an edge crack under uniform tension loading parameter for the crack opening function stress intensity factor reference stress intensity factors weight function parameters weight function non-dimensional&d stress distribution applied stress system associated with the reference stress intensity factor plate thickness crack opening displacements corresponding to the reference stress intensity factor K, distance from the crack mouth local stresses normal to the crack plane local reference stresses normal to the prospective crack plane and corresponding to the reference stress intensity factors K,, K,, , K, and K,, respectively characteristic stress or the nominal stress