The propagation of Alfvén waves from the photosphere into the corona with regard to the fine structure of the magnetic field is considered. The energy flux of Alfvén–type waves generated in the photosphere by convective motions does not depend on the ionization ratio. The reflection coefficient continuously decreases with a decrease of wave period. Influence of the external magnetic field on the Spruit cutoff frequency for transverse (kink) modes excited in the thin magnetic flux tubes is analyzed. Torsional modes can penetrate into the upper atmosphere most effectively since their amplitudes does not increase with height in the photosphere while kink ones can be transformed into shock waves in the lower chromosphere because of a significant increase of amplitudes. In spite of stratification the linearity of Alfvén–type modes in the chromosphere is conserved due to violation of the WKB approximation. The important role of the magnetic canopy is discussed. Alfvén waves generated by convective motions in the photosphere can contribute significantly to the heating of the coronal plasma in quite regions of the Sun.