This report gives a programme for the determination of the flow around a circular cone. Both the cases of zero-inclination and of a small inclination have been considered. The programme is written in the international machine language ALGOL and can therefore be operated on any computer having an ALGOL compiler. The purpose of this investigation was mainly to provide an accurate solution for these conical flows in view of their application as initial data along a "first characteristic". These data will enable the determination of the flow field around an axially symmetric configuration having a nose contour which may be considered as conical along a certain distance from the vertex. The programme is discussed in detail and some results obtained by it are included as an example.