Abstract: Aiming to address the limited investigation depth and inadequate azimuthal identification capability of logging-while-drilling (LWD) resistivity imaging tools in oil-based drilling fluid environments, a multi-frequency azimuthal lateral resistivity imaging logging structure with plate-type receivers is proposed. Based on the operating principle of the tool, an equivalent circuit model and a three-dimensional finite-element model are established. The models are validated using a homogeneous formation, and further simulations are carried out for a formation with four azimuthal sectors, a formation containing high- and low-resistivity anomalies, and an inclined layered formation. The response characteristics of the real and imaginary parts of the impedance under different frequencies, as well as the sensitive range of formation resistivity, are analyzed. In the homogeneous formation, the equivalent-circuit results agree well with the finite-element forward simulation results. In the azimuthally partitioned formation, the real and imaginary parts at low frequencies are more sensitive to variations in high- and low-resistivity layers, while high frequencies can assist in distinguishing layers with different resistivities. The anomaly-body model shows that the response amplitude increases with the azimuthal opening angle, and the real and imaginary parts are complementary. In the inclined layered formation, multi-frequency joint analysis can enhance the identification of layer interfaces and improve the stability of dip-angle calculation. The proposed multi-frequency azimuthal lateral resistivity imaging method can effectively characterize azimuthal electrical differences in complex formations, providing a model basis and methodological reference for imaging logging research under oil-based mud conditions.