In experiments colloidal crystals are usually polycrystalline. This polycrystallinity depends on the shear history, while a stable orientation of the crystallites is obtained by preshearing the sample for a sufficiently long time. To predict the linear viscoelastic properties of a colloidal crystal, the crystallites immersed in a Newtonian fluid are modeled by bead–spring cubes. Explicit constitutive equations are obtained, which describe the stress response on the applied small-amplitude oscillatory shear flow with frequency ω. These constitutive equations are used to predict the dynamic moduli G′(ω) and G″(ω) belonging to the specific configurations of the polycrystalline sample before and after preshearing. The influence of the preshear process on the dynamic moduli is discussed and for a sample that is presheared for a sufficiently long time the following results are obtained: (i) for high frequencies G′(ω) is constant and G″(ω) = η∞ω (where η∞ is the viscosity contribution of the fluid surrounding a crystallite) and (ii) for lower frequencies G′(ω) is nearly constant and G″(ω) is proportional to ω−1/2. The theoretical results obtained in this paper are consistent with experimental results found in literature. It is finally noted that the bead–spring formalism in this paper shows explicitly that the static modulus belonging to the crystallites is identical to the high frequency limit of the storage modulus G′(ω).