Respiratory gas exchange is intricately tied to the dynamic behavior of alveoli, minute and elastic air sacs nestled within the pulmonary system. These microstructures cyclically expand and compress with each breath, facilitating efficient gas exchange. Unfortunately, diverse pathological conditions can disrupt this vital process, leading to the accumulation of mucus and anomalous fluids, culminating in the debilitating condition known as pulmonary edema. Here, we aim to understand the interplay between fluid accumulation and the mechanical characteristics of alveoli, with the ultimate goal of shedding light on the underlying mechanisms for prompt diagnosis and intervention. To investigate how periodicities and geometries impact the mechanical attributes of lung tissue, we utilized 3D-printing technology to create soft elastic resin models mimicking the alveolar structure in various sizes. These models were subjected to rigorous uniaxial tension and compression tests at varying loading rates, allowing us to elucidate their material mechanical behavior. Next, to mimic the conditions observed in pulmonary edema, we filled 3D-printed alveoli samples (soft metamaterials) with glycerol solutions of different concentrations, yielding a range of viscosities and surface tensions. These fillings closely simulated scenarios involving blood or mucus accumulation. We conducted large-amplitude oscillatory shear (LAOS) rheometry tests to scrutinize how these filled liquids alter the apparent mechanical properties of lung tissue. In summary, this research endeavors to enhance the fundamental, scientific understanding of pulmonary edema etiology and progression, ultimately advancing expedited diagnosis and targeted therapeutic interventions. Furthermore, the insights gained from this work have the potential to inform advancements in artificial tissue bio-printing and contribute to the field of organ transplantation.