Since crack initiation in adhesive bonds tends to occur near the interface corners where the stress fields are singular, we define a fatigue initiation criterion using stress singularity parameter, Q (a generalized stress intensity factor) and the singular eigenvalue, lambda. Hattori ct al., successfully used a generalized stress intensity factor to characterize the static strength of bimaterial interfaces. We show that this criterion is only appropriate for situations in which the adhesive contact angle is no larger than 90 degrees and the modulus ratio (adhesive to adherend) is smaller than 0.1. Fortunately, these conditions are often met in real joints, permitting the use of a single eigenvalue approach. We then extend this criterion to the case of fatigue arising from mechanical, thermal, or hygroscopic cycling. In preparation for Part 2 (experimental), the special case of an epoxy wedge on a Rat aluminum substrate is considered. The singularity is analyzed both analytically and numerically. The scale of the region dominated by the singularity is found to be of the order of 100 mu m; The size of the plastically yielded zone near the apex is found to decrease extremely rapidly as the stress intensity factor goes down, thereby increasing the applicability of the method at the low stress levels often encountered in fatigue.