The miscibility of random copolymers (COP), consisting of dimethylsiloxane and methylphenylsiloxane units, with poly(dimethylsiloxane)s (PDMS) was studied in the absence and in the presence of shear experimentally as well as theoretically. Blends of COP 0.86 28 with PDMS 33 (subscripts: volume fraction of DMS in the copolymer, numbers after the abbreviations: weight average molar masses in kg/mol) were investigated far from critical conditions on the PDMS side of the phase diagram. According to these experiments the two phase regime increases by shear without exception and the maximum effects grow from 3 to 12 K as the PDMS concentration increases. Theoretical calculations were performed under the premise that shear destroys clusters of like segments formed under equilibrium conditions. The effects calculated in this manner are of the correct order of magnitude, but their concentration dependence contradicts the measurements. Blends of COP 0.71 7 with PDMS 27, PDMS 33, or PDMS 38 exhibit critical concentrations at approx. 23 wt.-% PDMS. For sufficiently low PDMS contents shear reduces the miscibility again according to experiment and theory. However, measurements demonstrate that the susceptibility of the blends towards shear decreases as the concentration of PDMS increases until the effect changes sign and the homogeneous region expands as the systems flow, in contrast to the calculations which yield a monotonous increase of shear effects. Possible reasons for the observed discrepancies are discussed.