Cosmological solutions are obtained in anisotropic Kantowski–Sachs (KS) and Bianchi Type-I Universes considering a cosmological constant with Skyrme fluid. Interestingly, the solutions obtained here in both the KS and Bianchi-I anisotropic Universes are found to isotropise at late time due to the presence of the Skyrmefluid, even in the absence of ʌ term or any inflationary mechanism involving the inflaton field. A comparative study of both the anisotropic cosmological models are carried out here and it is found that the Bianchi-I Universe admits oscillatory solutions for a given matter configuration.We also note that the emergent Universe model can be obtained with the Skyrme fluid. The anisotropy, deceleration and jerk parameters have been studied along with the linear perturbative stability to explore the efficacy of the models. Both cosmological models are stable in the absenceof cosmological constant. Besides, their predictions are compatible with the observational data. Thus, wemay claim that Skyrme fluid is a possible source of isotropization of an anisotropic Universe via accelerated expansion, whichis capable of reproducing some features that can be observed in the Universe.