Coal mass strength properties must be estimated to obtain realistic estimates of coal pillar strength. The limitations of existing techniques for approximating these properties are discussed. The coal mass is anisotropic. The Hoek and Brown approach to rock mass property estimation is modified to allow for this. This approach requires the Rock Mass Rating (RMR) for the strata. In the normal case where bedding is sub-horizontal, these major planes of weakness have little effect on the strength of pillars. As a result of this the RMR must be measured parallel to bedding. This means that a significantly higher rating than that usually obtained for coal is observed. The use of mass strength property estimates in extant empirical relationships is outlined. At high width to height ratios, an acceleration in the rate of increase in pillar strength with increasing width to height ratio has been observed. The empirical relationship developed by Salamon (the so called squat pillar formula) takes account of this. This relationship was found to have significant limitations with respect to its universal application. Modifications are made to Bieniawski's empirical formula to extend its use to large width to height ratio (squat) pillars. This new squat pillar formula has none of the disadvantages associated with Salamon's relationship. Strain softening was incorporated into non-linear finite difference numerical modelling to estimate pillar strengths. The technique outlined above is used to obtain peak coal mass properties. Modelled pillar strength was found to be sensitive to both peak and post peak mass strength properties. Post peak properties were found to be difficult to obtain and required some back analysis. Modelling results were used to estimate both the strength of squat pillars and parameters for use in a new squat pillar empirical strength relationship.