Analytical expressions for the stress growth coefficients in simple shear and extensional flows are developed for dilute suspensions of spheroidal particles. The orientation tensors used in the constitutive equation for suspensions are approximated as proposed by Currie [J. Non-Newt. Fluid Mech. 11, 53-68 (1982)]. The resulting rheological properties are found to be dependent on the components of a new, modified Finger strain tensor defined in terms of the velocity gradient tensor and particle aspect ratio (length to diameter ratio of the particle, a(p)). The approximate analytical results are presented as a function of total shear and elongation for different aspect ratios, covering the entire range from slender fibers (a(p) --> infinity) to thin disks (a(p) --> 0). In addition, exact integral expressions for the rheological properties are obtained from the orientation distribution function. The rheological properties evaluated from the approximate analytical expressions are found to be in excellent agreement with the corresponding results determined from the exact integral expressions.