Recent advances in two lifting surface methods are reported. The prese
nt subsonic constant pressure method improves upon the program robustn
ess of the doublet lattice method. The present unified supersonic-hype
rsonic method extends the range of applicability of lifting surf-ace t
heory to the Newtonian limit. Based on a uniformly-valid series formul
ation, the method accurately approximates the non-linear thickness eff
ect, whereas this effect is neglected by the linear theory and overest
imated by piston theory. In fact, the present results generally agree
well with the trends of several Euler solutions. Among other findings,
cases computed by the unified method confirm that the effect of thick
ness is to reduce the supersonic flutter speed.