In this study, two-phase density wave instability in parallel-twin rectangular channels was investigated with axially nonuniform heat profiles in the reactor core combined with static and rolling conditions. A parallel-channel thermal-hydraulic model was built using the method of two-phase homogeneous flow developed in previous work, while the drift-flux approach for void fraction and profile-fit model for subcooled boiling were implemented. Although the rolling condition was chosen as the typical motion in this work, the additional force caused by the motion with six degrees of freedom was derived. The theoretical analysis was performed based on the method of small power perturbation for parallel-twin rectangular channels. The flow oscillation caused by rolling was studied for different system parameters, including inlet resistance, exit resistance, pressure, and axial heating profile. The influence on flow instability of rolling parameters such as period, amplitude, and distance between channels was analyzed. The results showed that it would destabilize the system if a larger additional force was generated by rolling parameters. The influence of different axial heat profiles on flow instability was also studied under inlet-peaked, cosine-shape, and outlet-peaked heat fluxes. The coupling effect of rolling motion and axial nonuniform heating was finally studied. The stability boundaries under different conditions were compared to the inherent boundary under the static condition with uniform heating. The results indicated that the influence of nonuniform heating was more evident and should be paid more attention to.