The problem of flowing a Maxwell upper-convected fluid on a horizontal surface is considered here in two conditions. One is the condition in which the plate is made of a porous material, and another one when it is not. For each case, the analytical solution is found using a technique called homotopy perturbation method (HPM). The codes developed in Maple software program are employed for this purpose, and the profiles for velocity and temperature are obtained. The provided analytical solution for each condition is validated using the numerical simulation of the boundary value problem (BVP), and then, a comprehensive sensitivity analysis is carried out. According to the results, for each case, an excellent agreement between the numerical simulation and analytical solution is seen. Moreover, it is found that the skin friction coefficient has a downward trend for both conditions when Deborah goes up. Furthermore, increasing the porosity coefficient is accompanied by decrease in both drag force and hydraulic boundary layer. In addition, for the investigated conditions, having a higher porosity factor leads to an enhancement in the heat transfer, whereas a decrease in Deborah has the same effect.