In the paper, a new method for the analysis and design of lightning protection systems for constructions and buildings against direct strokes is presented. while the theory of the method is discussed in the paper, its applications are presented in a companion paper with the same heading: ‘Part 2: Applications’. The theory is based on the study of the critical field strength values in nonuniform fields, and its applications to an electromagnetics model of the lightning stroke. The main goal of the paper is to give the electrical engineer a tool for the determination of the parts of the structure and its vicinity, which are exposed to lightning strokes. The probability of strokes which may hit the structure is valuable information in the design of a reliable lightning protection system.