Recently, we have published (Vandas, 1994) an analytical solution for electron acceleration by a curved shock approximated by a cylinder or a sphere. However, real curved shocks (like the Earth's bow shock) are far from these ideal shapes, and this matter affects electron acceleration. We present a method for the calculation of electron acceleration by a curved shock wave of a general shape and find an analytical solution in a specific case with an application for the Earth's bow shock. We compare the theory for reflected electrons in two cases, for an interplanetary shock and for the Earth's bow shock. We get comparable levels of fluxes of 2--3 keV electrons at the interplanetary shock. Accelerated electrons above 10 keV at the Earth's bow shock have harder spectrum than follows from the theory. We suggest that some additional process (like pitch angle scattering) keeps the electrons longer in the shock layer and enables them to gain more energy. ¿ American Geophysical Union 1995