Mechanical properties of electrorheological fluids under various dynamical loading conditions have been studied using a computer simulation model. The model assumes electrostatic point-dipole interaction between particles with or without multipolar corrections and the interaction with the base fluid due to viscous laminar flow is described with Stokes drag. Mechanical loading is introduced as constant rate shear, compression or elongation to a system of particles set initially to a single chain, a column of body centered tetragonal (BCT) unit cells, a thick BCT structure or to a structure grown with electric field from originally random configuration. Results show that the single chain structure has usually the highest relative strength. Electrorheological systems under compressive loading were found to transmit the largest force from one plate to another. Under elongation loading a thick BCT structure seemed surprisingly weak compared with the system under compression or shear. In addition, the response of a BCT structure to sinusoidally alternating shear or tensile straining has been studied. Under tensile loading it was found that the ability of the system to transfer force is much more dependent on oscillation frequency than under shear loading.