In this paper, we present a classification of 2-designs with gcd(r,λ) = 1 admitting flag-transitive automorphism groups. If G is a flag-transitive automorphism group of a non-trivial 2-design D with gcd(r,λ) = 1, then either (D,G) is one of the known examples de- scribed in this paper, or D has q = pd points with p prime and G is a subgroup of AΓL1(q).
