Hygrothermal models for numerical simulation of heat and moisture transfer in building envelopes are already well developed and available to the scientific community. Building upon existing codes, the inclusion of air convection is an essential step towards realistic simulation of air permeable materials. Modeling the airflow effects on hygrothermal performance of vented roofs and lightweight wall assemblies is of particular practical relevance. Key element for an efficient numerical solution is the method of coupling of the balance equations for heat, air and moisture. Various numerical solution techniques exist for coupled non-linear systems of differential equations and have been successfully employed for solving two-dimensional coupled heat and moisture transport problems. However, finding an efficient solution scheme with acceptable accuracy for three-dimensional problems, including airflow effects, remains a challenge. The paper presents the governing equations and assumptions of a newly developed model for Coupled Heat, Air Moisture and Pollutant Simulation (CHAMPS). An approach for considering three-dimensional airflow effects is introduced. The capabilities of the numerical model are demonstrated by application to a vented roof construction widely used in moderate climate zones.