Under certain conditions, numerous internal surface cracks develop in pressurized thick-walled cylinders both in the radial and longitudinal directions. For fatigue life assessment of such vessels the 3-D interaction effects among these cracks on the prevailing stress intensity factors (SIFs) need evaluation. In part I of this paper radial crack arrays are considered exclusively. The Mode I SIF distribution for a wide range of semi-circular and semi-elliptical cracks are evaluated. The 3-D analysis is performed via the finite element method with the sub-modeling technique, employing singular elements along the crack front. SIFs are evaluated for arrays of up to n = 180 cracks; for a wide range of crack depth to wall thickness ratios, a/t, from 0.05 to 0.6; and, for various ellipticities of the crack, i.e., the ratio of crack depth to semi-crack length, a/c, from 0.2 to 2. Using a least squares fit, two simple expressions for the most critical (n = 2) SIFs are obtained for sparse and dense crack arrays. The formulae, which are functions of a/t and a/c, are of very good engineering accuracy. The results clearly indicate that the SIFs are considerably affected by the interaction among the cracks in the array as well as the three-dimensionality of the problem. In Part II of this paper, the interaction effects between longitudinal coplanar cracks will be analyzed.