The present study aims at analysing the sensitivity of two-dimensional flow past a flat plate to uncertain inflow conditions in the laminar flow regime. Both the Reynolds number and angle of incidence are treated as random inflow variables. The methodology consists of a stochastic collocation method based on generalised polynomial chaos (gPC) theory coupled with standard deterministic numerical simulations. With respect to the two random inputs, sensitivity analysis of global integral parameters such as Strouhal number, drag and lift coefficients and the time-averaged flow fields is performed, resulting in the construction of their response surfaces. The stochastic response of the full spectrum of the drag coefficient is also obtained. It is noticed that integral parameters are sensitive to the two random parameters. There is a peak in the probability density function (PDF) of mean drag coefficient. Two additional high frequencies are predicted in the spectrum of drag coefficients. They are about two and four times the primary vortex shedding frequency respectively, corresponding to first and second harmonics of the primary frequency. For the flow fields, the analysis demonstrates that the most probable solutions are significantly different from the deterministic ones and the solution sensitivity is localised near the regions transitioned to large scale fluid structure movements. Non-linear coupling between the two uncertainties is also studied thanks to the Sobol's decomposition. The angle of incidence is found to be the most influential variable to the mean flow fields.