In this note we prove that for any compact subset S of a Busemann surface (S, d) (in particular, for any simple polygon with geodesic metric) and any positive number δ, the minimum number of closed balls of radius δ with centers at S and covering the set S is at most 19 times the maximum number of disjoint closed balls of radius δ centered at points of S: ν(S) ≤ ρ(S) ≤ 19ν(S), where ρ(S) and ν(S) are the covering and the packing numbers of S by δ-balls. Busemann surfaces represent a far-reaching generalization not only of simple polygons, but also of Euclidean and hyperbolic planes and of all planar polygonal complexes of global non-positive curvature. Roughly speaking, a Busemann surface is a geodesic metric space homeomorphic to R 2 in which the distance function is convex.