A numerical investigation of structures of laminar liquid oxygen/hydrogen spray diffusion flames in the counterflow configuration is performed for high subcritical, cryogenic conditions. The dilute spray is modeled using Lagrangian equations; both mono- and bidisperse sprays are considered. The Eulerian formulation of the gas phase equations includes derailed transport and detailed chemical reactions which enables the investigation of both the inner flame structure and the extinction of these flames. The model includes transport coefficients for the gas phase for cryogenic temperatures and elevated pressure. Moreover, the formulation of thermodynamic equilibrium at the droplet surface includes both temperature and pressure dependence of the binary mixture, and it replaces the commonly used Raoult's law. The study presents parametric dependencies of the flame structure on equivalence ratio, strain rate, and dispersity of the spray, it appears that the Sauter mean diameter is a good approximation for describing the flame structure for the bidisperse spray flames at low strain.