Kinetic effects of Alfve´n wave spatial resonances near the plasma edge are investigated numerically and analytically in a linearized cylindrical tokamak model. In Part I, cold plasma surface Alfve´n eigenmodes (SAE’s) in a pure plasma are examined. Numerical calculations of antenna‐driven waves exhibiting absorption resonances at certain discrete frequencies are reviewed first. From a simplified kinetic equation, an analytical dispersion relation is then obtained with the antenna current set equal to zero. The real and imaginary parts of its roots, which are the complex eigenfrequencies, agree with the central frequencies and widths, respectively, of the numerical antenna‐driven resonances. These results serve as an introduction to the companion paper, Part II [Phys. Fluids B1, 2364 (1989)], in which it is shown that, in the presence of a minority species, certain SAE’s, instead of heating the plasma exterior, can dissipate substantial energy in the two‐ion hybrid layer near the plasma center.