Sediment-organic matrix composites are materials that exhibit complex mechanical behavior, particularly when subjected to different loading conditions. In many cases, the response to compression and tension are not symmetric, which poses challenges for accurate modeling using conventional criteria such as von Mises and Tresca. These traditional approaches do not account for the influence of hydrostatic pressure on material behavior, which is a critical factor for pressure sensitive materials. The aim of this work is to develop a pressure-dependent constitutive model for the Hemoglobin-Marine Sediment composites (HESM). This model is designed to predict the mechanical behavior of the composite under various loading conditions, with a specific focus on capturing the asymmetry between compression and tension responses. By incorporating hydrostatic pressure effects, the model aims to provide a more realistic representation of the material’s mechanical properties, improving the accuracy of simulations and structural predictions. The proposed approach involves characterizing the material’s response through experimental data and implementing a constitutive framework that integrates pressure sensitivity into accurately modeling the material’s mechanical behavior. In addition to their mechanical relevance, HESM composites are biodegradable biocomposites derived from natural materials. Its development contributes to reducing the use of traditional petrochemical-based matrix composites, promoting more sustainable and eco-friendly material alternatives for engineering applications.