In the paper, a linear differential equation with constant delayed arguments subject to a two-point boundary condition is considered on a finite interval. This problem is investigated by the Dzhumabaev parameterization method. By introducing parameters as values of the desired solution at the points of delays, the considered boundary value problem is reduced to an equivalent multipoint boundary value problem with parameters. Sufficient conditions of unique solvability of the multipoint boundary value problem with parameters are obtained in terms of initial data. A numerical algorithm for finding an approximate solution of the boundary value problem for a differential equation with delayed arguments is constructed.