The theory of the motion of a cleavage crack created by wedging open the ends of a double cantilevered crystal at a constant rate has been investigated. The results are presented for use in analysis of experimental studies of fracture dynamics in lithium fluoride reported in Part II of this series. A solution of the quasistatic equations of motion of the crack including kinetic energy effects has been found from which the dynamic fracture surface energies may be deduced for a propagating crack of this geometry by observations of either the time dependence of the crack length or the profile of the fracture opening near its tip. The detailed configurations of dislocations accompanying the tip of a moving crack in alkali halides have been calculated using dislocation dynamics and continuum elasticity theory. The plastic deformation contribution to the effective fracture surface energy has been determined and some of its consequences worked out.