The micrometer-scale length of some protein polymers allows them to be mechanically manipulated in single-molecule experiments. This provides a direct way to measure persistence length. We have used a double optical trap to elastically deform single microtubules and actin filaments. Axial extensional force was exerted on beads attached laterally to the filaments. Because the attachments are off the line of force, pulling the beads apart couples to local bending of the filament. We present a simple mechanical model for the resulting highly nonlinear elastic response of the dumbbell construct. The flexural rigidities of the microfilaments that were found by fitting the model to the experimentally observed force-distance curves are (7.1 +/- 0.8) x 10(4) pN nm2 (persistence length L(p) = 17.2 microm) for F-actin and (6.1 +/- 1.3) x 10(6) pN nm2 (L(p) = 1.4 mm) for microtubules.