• Cost effective optimisation of modified bitumen with liquid rubber for pavements and roofing membranes is presented. • Design optimisation technique allowed producing superior bituminous binders. • LR improves the flexibility at low in-service temperatures (using up to 50% contents), while EBS improves stiffness at high in-service temperatures. • The Response Surface Methodology was successfully used to optimise the final blends also in terms of cost. • Analytical functions amongst the design parameters have been derived and here provided for future design exercises. • The final properties were comparable to Polymer Modified Binders. Polymer Modified Bitumens (PMBs) are largely used for pavement and roofing membranes applications with Styrene-Butadiene-Styrene Block copolymer (SBS) playing a major role in both markets despite its constantly increasing price due to the rising demand for quality bitumen modifiers. On the other hand, there is an increasing trend of recycling end of life tyres generating Recycled Tyre Rubber (RTR) at affordable price. This investigation aims at engineering a modified bitumen with a combination of Liquid Rubber (LR), a homogeneous blend of 50–70% RTR pre-processed in combination with heavy oils, and a wax denominated Ethylene Bis Stearamide (EBS). In the first phase, the effect of LR and EBS was independently characterised and compared to PMBs. Next, the Response Surface Methodology (RSM) was used to predict the response of different combinations of LR and EBS in terms of low and high temperature properties and cost, to then be optimised targeting conventional and rheological properties of PMBs currently used in asphalt mixtures and roofing membranes in UK. As a result, an optimum combination of LR and EBS was found leading to a cost-effective modified bitumen comparable to PMBs. The work provided also analytical functions that could be of use in further design exercises. [ABSTRACT FROM AUTHOR]