Rammed earth (RE) is a venerable construction technique, gaining attention today owing to its environmental and sustainable qualities. A key obstacle to its wider adoption is a lack of strength characterisation methods to aid in design and conservation. Research over the past decade has demonstrated that suction is the key mechanism behind strength and strength gain. As suction changes with the building's environment, being able to predict strength changes with suction is essential for practitioners and conservators alike. This paper presents a method for predicting RE strengths based on the extended Mohr-Coulomb (EMC) framework. Construction of an EMC failure envelope in the residual suction range is discussed and the use of a planar envelope is justified. Unconfined compression and indirect tensile tests on two RE soils are used to construct this envelope and methods to predict strengths from it are derived. Excellent agreement between measured and predicted strengths is also found for available data in the literature. Simplifications are identified to adapt the developed technique to suit RE practice and a suitable experimental procedure is outlined. Finally, the revised experimental procedure is employed at an existing RE construction facility to successfully predict strengths of a compacted Californian sandy loam.