Amirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-2449Articles in Press20230930$K$-contact generalized square Finsler manifolds525710.22060/ajmc.2023.22528.1166ENHannanehFarajiDepartment of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), IranBehzadNajafi SaghezchiDepartment of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), IranTayebehTabatabaeifarDepartment of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), IranJournal Article20230704We study almost contact generalized square Finsler manifolds and introduce the notion of $K$-contact Finsler structures. Then, we characterize generalized square $K$-contact almost contact manifolds. As an application, we show that every $3$-dimensional Lie group admits a left-invariant generalized square Finsler structure.