The present invention provides hydrogenated β-pinene-based polymers with excellent heat resistance and light resistance, low absorptivity and high transparency, as well as molded articles thereof. The polymers of the present invention contain 50% by mass or more of β-pinene units and are hydrogenated β-pinene-based polymers where the ratio of the proton integral value at 6 to 8 ppm to the total proton integral value in a 1H-NMR spectrum is 2.3×10−5 or less or the p-phenylene group content is 0.0055% by mass or less, and the ratio of the proton integral value at 4.5 to 6 ppm to the total proton integral value is 2.8×10−4 or less or the cyclohexene-1,4-diyl group content is 0.29% by mass or less. The molded articles of the present invention contain the above hydrogenated β-pinene-based polymers.