During suction blow molding process, the extruded parison undergoes twisting deformation within the mold cavity, as the air drawing flow around the deforming parison exerts non-uniform shear stresses on its surface. Such twisting deformation can compromise the specific radial and circumferential variations in parison thickness that are intentionally generated during extrusion. This research is devoted in developing a fluid-structure interaction model for predicting parison deformation during suction blow molding process, with a specific emphasis on the suction stage. A fluid flow model, based on Hele-Shaw approximations, is formulated to simulate the air drag force exerted on the parison surface. The rheology of the material of the parison is assumed to obey the viscoelastic K-BKZ model. As the suction process also involves the sliding of the parison within the mold cavity, a modified Coulomb's law of dry friction is used to simulate the frictional contact between parison and mold. The numerical results of this study allowed identifying a clear correlation between the twisting deformation undergone by the parison during the suction stage, also observed experimentally and the design parameters, namely, the air drawing speed, the geometry of the duct mold cavity, and the parison/mold eccentricity. POLYM. ENG. SCI., 59:418-434, 2019. (c) 2018 Her Majesty the Queen in Right of Canada