A technique for the solution of the conically self-similar form of the Euler equations is described. Solutions for the flow past a flat-plate delta wing at angle of attack are presented. These solutions show strong leading edge vortices with large total pressure losses in the cores. A study of the effects of various computational parameters on the total pressure loss is made. An explanation for the cause of the total pressure loss is presented. It is shown to be consistent with the results for both a quasi-one-dimensional model problem and the conically self-similar flow past the flat-plate delta wing.