The wall design equations available in major codes of practice (e.g. AS3600 and ACI318) are intended for the design of normal strength concrete load bearing walls supported at top and bottom only. These codes fail to recognise any contribution to load capacity from restraints on the side edges. They also fail to give guidance on the applicability of the equations to high strength concrete. Further, they do not consider slender walls. In many situations walls have side edges restrained and are composed of high strength concrete with high slenderness ratios. The recognition of these factors in the codes would result in thinner walls and consequently savings in construction costs. In this thesis, the focus is on the development of a design formula and new design methods for axially loaded reinforced concrete wall panels. The design of walls having side restraints and being composed of high strength concrete is given particular attention. An experimental program has been undertaken to obtain data for the derivation of applicable formulae and to verify the analytical methods developed herein. Note that, the test results and other data available in published literature have also been used to develop the design formula. The formula encompasses effective length, eccentricity and slenderness ratio factors and is proposed for normal and high strength concrete walls simply supported at top and bottom only (one-way) and simply supported on all four sides (two-way). The major portion of the experimental program focuses on a series of normal and high strength concrete walls simply supported at top and bottom only (one-way), and simply supported on all four sides (two-way) with eccentric axial loading. The behaviour of the test panels is noted, particularly the difference between the normal and high strength concrete panels. A Layer Finite Element Method (LFEM) is used as an analytical tool for walls in two-way action. The LFEM gives comparable results to the test data and the proposed design formula. As part of the research, a program named WASTABT has also been developed to implement a more accurate analytical method involving the instability analysis of two-way action walls. WASTABT is proven to be a useful design tool in situations where the walls have (i) various reinforcement ratio in one or two layers; (ii) composed of normal or high strength concrete; (iii) various eccentricity.