During recent years, with the rapid development ofscience and technology in micro- and nano-measuring technologies, it hasbeen found that there are many significant differences in fluid flow atbetween macro-scale and micro/nano-scale, such as wall-slip phenomenon.Fluids exhibiting slip are important in technological applications.Therefore better understanding of the phenomenon of slip is necessary. Thispaper presents a theoretical analysis for the MHD stagnation-point flows ofan upper-convected Maxwell fluid towards a stretching sheet with slip．Thegoverning system of partial differential equations is first transformed intoa system of dimensionless ordinary differential equations. By using thehomotopy analysis method, a convergent series solution is obtained．Thereliability and efficiency of series solutions are illustrated by goodagreement with numerical results in the literature．Besides, the effects ofthe slip parameter, the magnetic field parameter, velocity ratio parameter,suction/injection velocity parameter and elasticity number on the flow areinvestigated. The flow and shear stress depend heavily on thevelocity slip parameter \gamma. Also, effect of increasing values of\gamma is to decrease the variation of |f''(0)| and the surface shear stress|f''(0)| is close to 0 with \gamma \to \infty. The dimensionless velocity f'(\eta)decreases with an increase in elasticity number \beta and \gammawhen velocity ratio parameter d is large than 1. However, an opposite behavior has been found when d<1.