Since the dislocation theory is introduced into the field of seismology, it has become possible to determine seismic source parameters, such as fault type, fault dimension, strike- and dip-angle, slip direction, rupture direction, rupture velocity, etc., from analysis of observed seismic waves. In these studies so far only surface wave data in far field are usually used because rather simple theoretical approach is possible for surface waves. It is easily supposed that seismic data in near field contain much informations on focal process than those in far field. Theoretical studies on seismic waves in near field, however, have not been thoroughly investigated as yet.The object of this study is to clarify characteristics of seismic waves in near field generated from a double couple source with an arbitrary orientation. Expressions for Laplace transforms of surface displacements with respect to time are obtained in a cylindrical coordinate system and applying Cagniard's method exact transient solutions are found when source time function is a ramp-type. It is shown that the moving source solution can be obtained by accomplishing numerical integration of the point source solution with some transformation of axes.In part I of this paper, mathematical expressions are derived and result of numerical computations and discussions are presented in part II.