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Plant-based concrete is a construction material which, in addition to having a very low environmental impact, exhibits excellent hygrothermal comfort properties. It is a material which is, as yet, relatively unknown to engineers in the field. Therefore, an important step is to implement reliable mass-transfer simulation methods. This will make the material easy to model, and facilitate project design to deliver suitable climatic conditions. In recent decades, numerous studies have been carried out to develop models of the coupled transfers of heat, air and moisture in porous building envelopes. Most previous models are based on Luikov's theory, considering mass accumulation, air and total pressure gradient. This theory considers the porous medium to be homogeneous, and therefore allows for hygrothermal transfer equations on the basis of the fundamental principles of thermodynamics. This study presents a methodology for solving the classical 1D (one-dimensional) HAM (heat, air, and moisture) hygrothermal transfer model with an implementation in MATLAB. The resolution uses a discretization of the problem according to the finite-element method. The detailed solution has been tested on a plant-based concrete. The energy and mass balances are expressed using measurable transfer quantities (temperature, water content, vapor pressure, etc.) and coefficients expressly related to the macroscopic properties of the plant-based concrete (thermal conductivity, specific heat, water vapor permeability, etc.), determined experimentally. To ensure this approach is effective, the methodology is validated on a test case. The results show that the methodology is robust in handling a rationalization of the model whose parameters are not ranked and not studied by their degree of importance.