A mathematical study of heat and flow of couple stress MHD fluids over permeable stretching/shrinking surfaces is undertaken in the present paper. Exact solutions for both flow and temperature fields under a boundary layer approach are targeted. In the absence of couple stress field the results completely collapse onto the special cases available in the literature. Obtained closed form solutions provide valuable knowledge for the velocity and temperature profiles as well as skin friction coefficient and Nusselt number. Dissimilar to the already known for a noncouple Newtonian fluid, double solutions exist over a stretching sheet, and triple solutions are present over a shrinking sheet, if couple stress effects are taken into consideration. (c) 2014 Elsevier Ltd. All rights reserved.