A combined theoretical and numerical study is carried out to quantify the influence of material properties (e.g., real part and loss factor of Young’s modulus, material density) and geometrical parameters (e.g., layer thickness, height of hole) on the sound absorption performance of an underwater rubber layer containing periodically distributed axial holes. A theoretical model is developed based on the method of transfer matrix as well as the concept of equivalent layering of holes with variable cross section. Numerical simulations with the method of finite elements are subsequently carried out to validate the theoretical model, with good agreement achieved. Physical mechanisms underlying the enhanced acoustic performance of the anechoic layer as a result of introducing the periodic holes are explored in terms of the generated transverse waves and the high-order mode of vibration. The results presented are helpful for designing high-performance underwater acoustic layers with periodically distributed cavities by tailoring relevant material properties and geometrical parameters.