A web-core steel sandwich panel is a lightweight structure where thin plates are welded together by laser-welding technique. The plates form a T-joint which has in the center a weld thinner than the plates themselves. Thus the rotational stiffness of the joint is not infinite. The paper investigates the influence of T-joint rotational stiffness on the lowest natural vibration frequency of the panel. The methods used in the study have different kinematic assumptions. Equivalent single-layer (ESL) theory is used to obtain the frequency of the global vibration. The local vibrations are predicted using an isolated part of the panel, the I-beam model. In addition, three-dimensional model of a sandwich panel is analyzed. Finite element method (FEM) and analytical solution are used to obtain the frequencies. First-order shear deformation theory (FSDT) is used. The joint is considered through its rotational stiffness whose quantitative values are presented in the literature. Four different cross-sections with industrial relevancy are considered. The rotational stiffness of the T-joint affects the transverse shear stiffness of the panels. The results show up to 22% reduction of the fundamental frequency when compared with the case of the rigid joint for the global vibration mode. The effect on local vibrations is up to 11% in the case of asymmetric rotation in the T-joint and is otherwise insignificant. The study furthermore outlined the limitations of the ESL approach for assessment of natural frequencies in web-core sandwich panels depending on the vibration mode shape. The results show that the rotational stiffness of the T-joint has to be considered in the conceptual design of these structures.