We report on the application of an electrostatic ion beam trap as a mass spectrometer. The instrument is analogous to an optical resonator; ions are trapped between focusing mirrors. The storage time is limited by the residual gas pressure and reaches up to several seconds, resulting in long ion flight paths. The oscillation of ion bunches between the mirrors is monitored by nondestructive image charge detection in a field-free region and mass spectra are obtained via Fourier transform. The principle of operation is demonstrated by measuring the mass spectrum of trapped Ar+ and Xe+ particles, produced by a standard electron impact ion source. Also, mass spectra of heavier PEGnNa+ and bradykinin ions from a pulsed MALDI ion source were obtained. The long ion flight path, combined with mass-independent charge detection, makes this system particularly interesting for the investigation of large molecules.