In elasticstatic mechanics there are the least potential principle and the least remaining principle, which is only applicable to the situation of the stable and equilibrium state. But generally speaking there are no stable and equilibrium state in dynamic problems, so it is worthwhile considering carefully whether there is the least potential principle in the dynamic field. This paper studied the possibility of the least potential principle existing in dynamic problems, and derived the least potential principle and the least remaining principle based on the least work consumption principle, which get rid of the limitations of “equilibrium" and “stable state". The practical calculating examples were proposed and the results were correct. So in linear elastodynamics there also exist the least potential principle and the least remaining principle in instantaneous sense, which have different physical meaning. The physical meaning of the former is to take “the minimum of all probable value meantime" at any moment in the dynamical process，and the latter is to take “the minimum" in the whole dynamical process. That is to say, the former is “the minimum at that time" and the latter is “the minimum in the whole process". These two variational principles may become the theoretical foundation for all sorts of variational direct solving methods in linear elastodynamics.