The goal of this work is to develop a numerical model for the vibration of hybrid electric vehicle (HEV) battery packs to enable probabilistic forced response simulations for the effects of variations. There are two important types of variations that affect their structural response significantly: the prestress that is applied when joining the cells within a pack; and the small, random structural property discrepancies among the cells of a battery pack. The main contributions of this work are summarized as follows. In order to account for these two important variations, a new parametric reduced order model (PROM) formulation is derived by employing three key observations: (1) the stiffness matrix can be parameterized for different levels of prestress, (2) the mode shapes of a battery pack with cell-to-cell variation can be represented as a linear combination of the mode shapes of the nominal system, and (3) the frame holding each cell has vibratory motion. A numerical example of an academic battery pack with pouch cells is presented to demonstrate that the PROM captures the effects of both prestress and structural variation on battery packs. The PROM is validated numerically by comparing full-order finite element models (FEMs) of the same systems. (C) 2014 Elsevier B.V. All rights reserved.