The problems for elliptical cracks situated in an infinite elastic solid and subjested to static and time-harmonic loads are considered. Traction boundary pseudodifferential equations are used for the solution to the problems. An analytical method is developed for the solution to the equations. The method leads to the constructive procedure for obtaining analytical solutions in the case of arbitrary static polynomial loads. If the loads are time-harmonic and their amplitudes can be expanded in the power series by the wave number with polynomial coefficients in the range of low frequencies then the method leads to the procedure of the expansion of the solution into the Taylor's series by the wave number. This class of loads includes particularly the loads corresponding to the problems of scattering plane longitudinal and shear waves obliquely incident to the crack surface. Taylor's series expansion is an accurate approximation of the solution only for low wave numbers. Pade approximants extend the range of accurate approximation of the solution from low to intermediate, wave numbers.
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