Hybrid electrical energy storage (HEES) systems consisting of heterogeneous electrical energy storage (EES) elements are proposed to exploit the strengths of different EES elements and hide their weaknesses. The cycle life of the EES elements is one of the most important metrics. The cycle life is directly related to the state-of-health (SoH), which is defined as the ratio of full charge capacity of an aged EES element to its designed (or nominal) capacity. The SoH degradation models of battery in the previous literature can only be applied to charging/discharging cycles with the same state-of-charge (SoC) swing. To address this shortcoming, this paper derives a novel SoH degradation model of battery for charging/discharging cycles with arbitrary patterns. Based on the proposed model, this paper presents a near-optimal charge management policy focusing on extending the cycle life of battery elements in the HEES systems while simultaneously improving the overall cycle efficiency.