This paper reviews contemporary rules in CSA S16:19, AISC 360-16 and EN 1994-1-1 for concrete-filled hollow structural sections (HSS), covering materials, cross-section classification, and concentrically loaded columns. Results from 453 tests on axially compressed concrete-filled HSS members are compared to predicted strengths using current (CSA S16:19, AISC 360-16 and EN 1994-1-1) and recommended CSA S16 design equations (with limits of validity), and a first-order reliability analysis is performed in accordance with CSA S408-11. The recommendations herein are shown to maintain the current CSA S16:19 Clause 18.2 level of reliability for concrete-filled HSS compression members. Design examples are provided, and results are compared to the counterpart American code (AISC 360-16). This paper is Part I of a two-part series. Part II covers flexural members, beam-columns, tension and shear.