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The variational einbein field method is applied to the model of the QCDstring with quarks at the ends for the case of light-light and heavy-lightmesons. Special attention is payed to the proper string dynamics. The correctstring slope of the Regge trajectories is reproduced for light-light stateswhich comes out from the picture of rotating string. Masses of severallow-lying orbitally and radially excited states in the D, D_s, B, and B_s mesonspectra are calculated and a good agreement with the experimental data as wellas with recent lattice calculations is found. The role of the string correctionto the interquark interaction is discussed at the example of the identificationof D*'(2637) state recently claimed by DELPHI Collaboration. For theheavy-light mesons the standard constants used in Heavy Quark Effective Theoryare extracted and compared to the results of other approaches.Comment: 4 pages, 3 EPS figures, uses epsfig.sty, specialized style files  included. Talk given at the 9th International Conference On Hadron  Spectroscopy (Hadron 2001), Protvino, Russia, 25 August - 1 September 2001,  to appear in Proceeding

Light-light and heavy-light mesons in the model of QCD string with quarks at the ends