This paper discusses the construction of polynomial and non-polynomial splines of the fourth order of approximation. The behavior of the Lebesgue constants for the left, the right, and the middle continuous cubic polynomial splines are considered. The non-polynomial splines are used for the construction of the special central difference approximation. The approximation of functions, and the solving of the boundary problem with the polynomial and non-polynomial splines are discussed. Numerical examples are done.