  The variational einbein field method is applied to the model of the QCD
string with quarks at the ends for the case of light-light and heavy-light
mesons. Special attention is payed to the proper string dynamics. The correct
string slope of the Regge trajectories is reproduced for light-light states
which comes out from the picture of rotating string. Masses of several
low-lying orbitally and radially excited states in the D, D_s, B, and B_s meson
spectra are calculated and a good agreement with the experimental data as well
as with recent lattice calculations is found. The role of the string correction
to the interquark interaction is discussed at the example of the identification
of D*'(2637) state recently claimed by DELPHI Collaboration. For the
heavy-light mesons the standard constants used in Heavy Quark Effective Theory
are extracted and compared to the results of other approaches.
