Exact solutions in closed form have been found using the eigenfunction-expansion method for various linear and quadratic flows of an unbounded incompressible viscous fluid at low Reynolds number past a porous sphere with a uniform permeability distribution. The linear flows considered here are a simple shear and an axisymmetric uniaxial straining flows and the quadratic flows include a unidirectional paraboloidal and a stagnation-like flows as typical representations. The theoretical analysis determines a general motion of a freely suspended particle in the prescribed mean flow at infinity. Then the solutions are expressed in terms of fundamental singularity solutions for Stokes flow which will be applied to examine the motion of a porous sphere in the presence of a plane fluid-fluid interface in the forthcoming part of the present paper.