We would like to define the notion of geodesics on surfaces with singular points. It is not suitable to define geodesics on surfaces with singular points by using a direct generalisation of geodesics for regular surfaces. As surfaces with singular points, we consider framed sur faces and generalised framed surfaces. Moreover, as curves with singular points, we consider framed curves. Then we give definitions of geodesics as framed curves on framed surfaces and generalised framed surfaces. We investigate properties of the geodesic and give examples.