A new structure classification scheme for biopolymers is introduced, which is solely based on main-chain dihedral angles. It is shown that by dividing a biopolymer into segments containing two central residues, a local classification can be performed. The method is referred to as DISICL, short for Dihedral-based Segment Identification and Classification. Compared to other popular secondary structure classification programs, DISICL is more detailed as it offers 18 distinct structural classes, which may be simplified into a classification in terms of seven more general classes. It was designed with an eye to analyzing subtle structural changes as observed in molecular dynamics simulations of biomolecular systems. Here, the DISICL algorithm is used to classify two databases of protein structures, jointly containing more than 10 million segments. The data is compared to two alternative approaches in terms of the amount of classified residues, average occurrence and length of structural elements, and pair wise matches of the classifications by the different programs. In an accompanying paper (Nagy, G.; Oostenbrink, C. Dihedral-based segment identification and classification of biopolymers II: Polynucleotides. J. Chem. Inf. Model. 2013, DOI: 10.1021/ci400542n), the analysis of polynucleotides is described and applied. Overall, DISICL represents a potentially useful tool to analyze biopolymer structures at a high level of detail.