The effect of a layer of low-rigidity sediments on the propagation of seismic waves across oceanic areas was investigated theoretically in an attempt to explain some of the observed features of surface wave propagation in the period range 5 to 20 seconds. In this period range theory shows that surface waves corresponding to propagation in Love modes and in certain shear modes are very sensitive to the shear velocity and thickness of a low-rigidity sedimentary layer. When this layer is present, two quite different families of shear modes are possible in the velocity range of interest here. One family of modes, similar to the fundamental Rayleigh mode and present also for the case of a non-rigid sedimentary layer, is controlled primarily by P waves multiply reflected in the water and sedimentary layer. These modes exhibit large amplitudes in the water and smaller amplitudes in the sediments. The other family of shear modes exists only when the sediments have finite rigidity and is controlled primarily by multiply-reflected SV waves in the sedimentary layer in much the same manner as the Love modes are controlled by SH waves. Particle amplitude-depth profiles show that modes of this family exhibit large amplitudes in the sediments and smaller amplitudes in the water and correspond to interface waves in the sense that maximum amplitudes are found at the water-sediment interface. The conversion of energy from P to SV and vice versa for angles of incidence corresponding to the normally dispersed portions of these two families of modes is very small at either sedimentary interface. This results in the separation into the two wave types. Most of the energy in these two families of modes, however, is propagated in the crust and upper mantle. Certain conversion of P to SV waves in deep-sea refraction work can also be explained by examining the energy transmission and reflection coefficients at the interfaces of a sedimentary layer. In addition to the above normal modes, a family of highly dispersed leaking modes may occur when a low-rigidity sedimentary layer is present. The results of this study are used in the following paper (Part II) in conjunction with experimental data.