We study the production of dark photons with masses in range 0.4-1.5\,GeV in elastic proton bremsstrahlung. In contrast to the known approaches to calculating the bremsstrahlung cross section, we consider the non-zero momentum transfer between protons. The numerical estimates show that the refined result agrees well with the generalized Weizsacker-Williams approximation, although it significantly differs from the result obtained by Blumlein and Brunner \cite{Blumlein:2013cua} which is widely used in proton beam-dump phenomenology.