This first part of two companion papers deals with the numerical modeling of timber-concrete composite beams (TCCs) under long-term loading. All phenomena affecting the long-term behavior of timber, concrete, and the connection system, such as creep, mechanosorptive creep, shrinkage/swelling, and temperature variations, are fully considered. The structural problem is solved through a uniaxial finite element model with flexible connection and a step-by-step numerical procedure over time. The important role played by the environmental thermohygrometric variations on TCCs is highlighted through some analyses. The proposed numerical procedure is validated on two long-term experimental tests in outdoor conditions. Despite some uncertainties in environmental conditions and material properties, a good fit between experimental and numerical results is obtained. A parametric analysis is performed in the second part, showing the contribution of different rheological phenomena and thermohygrometric variations on beam deflection and connection slip. Based on results carried out, a simplified approach for long-term evaluation of TCCs is then proposed.