A molecular model is presented for triacylglycerides. These molecules are the main constituent of natural oils, and they are being increasingly sought out for novel technological applications (e.g. in high-performance, biodegradable lubricants). The model is derived from a combination of quantum-mechanical calculations, molecular simulations, and comparisons to experiment. It is shown to be capable of describing a number of equilibrium thermodynamic and transport properties for pure triacylglycerides and their mixtures. Calculated densities and viscosities are in good agreement with available experimental data. Predictions of the viscosity of several multicomponent mixtures, such as canola oil, cocoa butter, and commercial-grade lubricants, also show good agreement with reported values. The proposed model is also used to explore relations between the structure and properties of different functionalities (e.g. position of ethyl branches along the main chain), thereby providing insights into how some chemical treatments might alter the physical properties of natural oils.