In this research, we study self-similar vector fields in Bianchi type III spacetime by applying
 the Rif tree method. This study uses a computer approach to convert symmetry equations
 into a simplified involutive form, which separates the integration problem into several cases
 that are shown as a tree structure. Certain restrictions apply to the metric functions in
 certain circumstances. Explicit formulations for the metrics and their corresponding self
similar vector fields are obtained by solving the system of equations governing self-similar
 symmetries using these conditions. Additionally, physical significance are taken into ac
count for an in-depth analysis of the generated models.