Pressure shifts and collisional narrowing effects of the molecular hydrogen (H2) 4-0 and 5-0 vibration rotation bands have been studied in greater detail than before. A high-resolution ring dye laser has been coupled to a multi-pass absorption cell with a base length of 22 m at Denison University in Granville, Ohio. Signal averaging periods of several hours, with an absorbing layer of 24 km-atm, were required to obtain acceptable measurements. A zero-density position and shift coefficient of 15 535.7441 ± 0.0036 cm-1 and -6.29 ± 1.29 × l0-3 cm-1/Amagat, respectively, have been determined for the 4-0 S(0) line. For the 4-0 S(1) line the corresponding values are 15 699.8011 ± 0.0010 cm-1 and -4.22 ± 0.36 × 10-3 cm-1/Amagat. The 5-0 S(1) line has been observed in the laboratory for the first time; its position has been located at 18 907.5160 ± 0.0200 cm-1. Linestrengths were also determined in this study and the results are 2.31 ± 0.55 × l0-5 cm-1/(km Amagat) for the 4-0 S(0) line, 1.37 ± 0.17 × l0-4 for the 4-0 S(1)line, and 1.76 ± 0.99 × 10-5 for the 5-0 S(1) line. Collisional narrowing was clearly evident for the 4-0 S(0) and 4-0 S(1) lines. © 1993 Academic Press, Inc.