[en] A program (TRISIM3D) for studying collective effects due to the impedance of structures along the vacuum chamber of particle accelerators and storage rings is developed; these effects may deterioriate the quality and stability of the beam. Previous programs were only 2-dimensional, they accounted for one transverse and the longitudinal space coordinate. Here the particle distribution in all three dimensions is expanded into triangular basis functions. Tables of the wake potentials of these basis functions are prepared by programs using mesh finite integration of the field equations (MAFIA or ABCI). Properties of wake fields in non-axisymmetric structures are studied in detail. In axisymmetric structures the main component is a dipole field; shielded bellows, electrostatic separators and other axially unsymmetric structures produce an additional quadrupole component. The wake potentilas excited in structures of the large electron positron collider (LEP) of CERN could be calculated only for bunch lengths, which were too long for use in TRISIM3D. As a new method a decomposition technique was developed to calculate the wake potentials of short bunches from those of larger ones. Results of 3-dimensional simulations of LEP including effects of wake potentials are presented. The computed ratio of horizontal and vertical tune-shifts agree with those obtained from measurements. (author)