Edge-localized compressional Alfven eigenmodes (CAE) may be responsible for the observed emission in the ion cyclotron frequency range in the National Spherical Torus experiments (NSTX) [M. Ono , Nucl. Fusion 40, 557 (2000)]. These modes can be driven unstable by resonant interaction with a small population of energetic ions, having an anisotropic distribution in velocity space. In the present paper, the radial and poloidal structure of these eigenmodes is analyzed, by solving the eigenmode equation using a variational approach. The analysis shows that CAE are radially and poloidally localized near the plasma edge and have eigenfrequencies in the range corresponding to experimentally measured frequencies in NSTX. (C) 2003 American Institute of Physics.