We deal with strongly elliptic differential operators of an arbitrary even order 2m with constant real coefficients and introduce a notion of the regularity of a boundary point with respect to the Dirichlet problem which is equivalent to that given by N. Wiener in the case of m = 1. It is shown that a capacitary Wiener's type criterion is necessary and sufficient for the regularity if n = 2m. In the case of n > 2m, the same result is obtained for a subclass of strongly elliptic operators.