  Formation of oblique solitons by a flow of polariton condensate past an
obstacle is considered. The flow is non-uniform due to a finite life-time of
polaritons what changes drastically the conditions of formation of oblique
solitons compared with the atomic condensate case. The theory shows that the
polariton solitons can be generated by a subsonic flow in agreement with the
recent experiment [A. Amo {\it et al.}, Science, {\bf 332,} 1167 (2011)].
Geometric form of oblique solitons and other their parameters are calculated
analytically and analytical results are confirmed by numerical simulations.
