An explicit solution is provided for the scattering of an obliquely incident flexural-gravity wave by a narrow straight-line crack separating two semi-infinite thin elastic plates floating on water of finite depth. By first separating the solution into the sum of symmetric and antisymmetric parts it is shown that a simple form for each part can be derived in terms of a rapidly convergent infinite series multiplied by a fundamental constant of the problem. This constant is simply determined by applying an appropriate edge condition. Curves of reflection and transmission coefficients are presented, showing how they vary with plate properties and angle of incidence. It is also shown that in the absence of incident waves and for certain relations between their wavelength and frequency, symmetric edge waves exist which travel along the crack and decay in a direction normal to the crack.