It is demonstrated that for classical perovskites, such as BaTiO3; SrTiO3, and PbTiO3, electrostrictive strain induced by an electric field may not obey traditionally considered "extension along the field and contraction perpendicular to it" behavior if the applied electric field is directed obliquely to the cubic crystallographic directions. A remarkable behavior is predicted for bars of BaTiO3; SrTiO3, and PbTiO3 cut along the [111] crystallographic cubic direction. In this case, in the paraelectric phase in an electric field parallel to the bar, some expansion along all its three dimensions is expected. The situation with the [110] cut is also unusual; the electrostrictive effect in a field along the bar will result in a contraction in one transversal direction and an expansion in the other. In terms of the effective "polarization-strain" electrostrictive coefficients of the sample, this means a positive transversal electrostriction coefficient for some sample orientations. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4764046]