There has been a keen interest in recent times on implementation of lightweight materials in vehicles to bring down the unladen weight of a vehicle for enhancing fuel efficiency. Fiber-reinforced composites comprise a class of such materials. As sustainability is also a preoccupation of current product development engineers including vehicle designers, bio-composites based on natural fibers are receiving a special attention. Keeping these motivations of lower effective density, environment friendliness and occupational safety in mind, woven jute fabric based composites have been recently studied as potential alternatives to glass fiber composites for structural applications in automobiles. In the past, mechanical characterization of jute-polyester composites were restricted to obtaining their stress-strain behaviors under quasi-static conditions. In the present study, coupon specimens extracted from jute-polyester laminates have been tested in a computer-controlled servo-hydraulic UTM at cross-head speeds (up to 500 mm/min) higher than quasi-static (not exceeding 1 mm/min). Even though the considered dynamic strain rates would lie in a low range, the effect of strain rate on stress-strain curves is clearly seen in the form of increasing tensile failure strength with respect to increasing strain rate. In order to shed light on the effect of strain rate on compressive behavior of the considered jute composite, cylindrical and square tubes made of the same material are subjected to drop-weight impact tests by varying the impactor drop height i.e. effectively the initial impact velocity. It is observed that the peak compressive load (related to laminate compressive strength) generated in a tube increases with an increase in impact speed. Thus, strain rate appears to have a perceptible effect on both tensile and compressive strengths of jute-polyester composites and should be perhaps taken into account in numerical prediction of the behaviors of such composites under impact loads.