The study of generalized Newtonian fluid (GNF) is a topic of practical interest in fluid mechanics. The GNF is non-Newtonian in nature, although its constitutive equation is generalized form of Newtonian fluid. Researchers are devoting their studies to explore different subclasses of GNF. Despite of the abundant research work in this field, an important subclass of GNF namely the Cross fluid has not been given due attention. The objective of this research work is to concentrate on the flow and heat transfer characteristics of Cross fluid. The inaugural work has been presented in this thesis by bestowing the boundary layer equations of Cross fluid in different coordinate systems. This has opened new doors for researchers to carry out further research in this direction. In this thesis, a theoretical study is done to explore the flow and heat transfer characteristics of Cross fluid. The reported work presents the modelling of the boundary layer equations of GNF using the Cross viscosity model and further bestows the numerical solution regarding these equations. The current research work covers the flow of Cross fluid past a planer as well as radially stretching sheet and stretching cylinder. Moreover, investigations are done on the mixed convection flow, Falkner-skan flow, nano boundary layer flow and stagnation point flow of Cross fluid. Several effects are taken into consideration including the impact of activation energy, melting phenomenon, linear and non-linear radiation, heat generation/absorption, multiple slip effects, variable thermal conductivity, Newtonian heat and mass conditions. The modelled problems are numerically handled by two numerical techniques namely the shooting method and bvp4c in MATLAB. The results presented in this thesis are verified by making comparison with already available results in literature for reduced cases and excellent compatibility is achieved. From the obtained results, it is observed from that the progressive value of the local Weissenberg number reduces the velocity distribution while the temperature of the fluid rises. However, quite an opposite trend is exhibited by velocity and temperature profiles for growing values of the power-law index.