Psoriasis, a persistent inflammatory condition with a complex origin, lacks a definitive cure despite the availability of diverse treatments. Vetpalai thailam (VT), a Siddha formulation, is commonly used for addressing various skin ailments. Analysis via GC-MS of a sample of VT oil unveiled the existence of 65 compounds. These identified phytochemical structures were then examined through molecular docking against the proinflammatory cytokines TNF-α and IL-17A, resulting in the shortlisting of seven compounds. Among these, four displayed binding potential against TNF-α, while three exhibited similar potential against IL-17A. Further, the individual shortlisted phytochemical and protein complexes were subjected to molecular dynamics and documented their RMSDs, RMSFs, SASA, Rg, MMPBSA, and PCA profiles. Other informatics web tools were employed to predict physicochemical properties, bioactivity, drug-likeness, and toxicity scores. Three compounds identified from VT oil displayed binding potential against IL-17A, showcasing binding energies varied between -8.427 and -6.739 kcal/mol, while four compounds exhibited potential against TNF-α, with binding energies ranging from -9.873 to -8.644 kcal/mol. The physicochemical attributes, bioactivity, compliance with Lipinski's rule of five, and ADMET profiles of the shortlisted compounds demonstrated favorable pharmacokinetic characteristics. Consequently, this research provides valuable insights into the binding ability of phytoconstituents of VT oil against IL-17A and TNF-α, paving the way for the development of novel drugs for the treatment of psoriasis.