The study presents a comprehensive analysis of welded joints by applying advanced mathematical modelling and experimental research methods. The primary objective was to develop and validate a methodology for mathematical modelling of the behaviour of welded joints under mechanical loading, as well as to assess the effectiveness of the proposed approaches in predicting their strength and durability. Based on the research results, we can draw the following conclusions. The authors obtained the results of welded joint samples and analysed the corresponding curves of the dependence of force factors on their deformations. The study showed that the destruction of welded joints occurs mainly along the weld seam, where the strength is lower than in the base material of the rods. It is consistent with the practical data of the experiment, which confirms that the weld is the weakest link in the structure. The article substantiated a set of provisions and assumptions for implementing mathematical modelling of the behaviour of samples of welded joints imitating welded joints in a reservoir for petroleum products under mechanical tensile tests. The test results justified the mathematical models of the steel material of welded joints of petroleum product tanks and obtained numerical parameters of the mechanical properties of steel of welded joints. Yield strength is in the range of 240–300 MPa, the modulus of elasticity is 190–240 GPa, the hardening modulus is 18–20 GPa, and the ultimate plastic deformation is 0.00334. Based on a complex of well-founded mathematical models of welded joints, we carried out calculations regarding the numerical study of the behaviour of welded joints under the conditions of their mechanical tests. We compared the obtained results with the results of experimental tests and, based on this comparative analysis, established that they were adequate since the Fisher criterion did not exceed the tabular value and the relative error did not surpass 12%. The findings of this research offer valuable insights and practical recommendations for improving the design and evaluation of welded structures, enhancing their performance and safety in engineering applications.