Despite the increased expenditure of the pharmaceutical industry on research and development, the number of drugs for cardiovascular diseases that reaches the market is decreasing. A major issue is the limited ability of the current in vitro and experimental animal models to accurately mimic human heart disease, which hampers testing of the efficacy of potential cardiac drugs. Moreover, many non-heart-related drugs have severe adverse cardiac effects, which is a major cause of drugs’ retraction after approval. A main hurdle of current in vitro models is their inability to mimic the stiffness of in vivo cardiac tissue. For instance, poly(styrene) petri dishes, which are often used in these models, have a Young’s modulus in the order of GPa, while the stiffness of healthy human heart tissue is <50 kPa. In pathological conditions, such as scarring and fibrosis, the stiffness of heart tissue is in the >100 kPa range. In this study, we focus on developing new membranes, with a set of properties for mimicry of cardiac tissue stiffness in vitro, based on methacrylate-functionalized macromers and triblock-copolymers of poly(trimethylene carbonate) and poly(ethylene glycol). The new membranes have Young’s moduli in the hydrated state ranging from 18 kPa (healthy tissue) to 2.5 MPa (pathological tissue), and are suitable for cell contraction studies using human pluripotent stem-cell-derived cardiomyocytes. The membranes with higher hydrophilicity have low drug adsorption and low Young’s moduli and could be suitable for drug screening applications.