In this paper, the quantitative flexibility of EH is evaluated considering a flexibility index which is based upon available maximum capacity as well as the response time of generating units. Here, the impact of simultaneous EH operation and construction are investigated on quantitative flexibility considering both uncertain supply and demand side resources. Hence, a new structure so-called multi-objective simultaneous operation/construction optimization of multi-carrier EH is presented ( soco MC MOF-EH ) which consists of a decrease in operation and construction costs as well increase in power system flexibility. The demand side uncertainties, including thermal/electrical demand, are implemented by the Gaussian distribution function, and uncertainty on the supply side, including gas pressure uncertainty (GPU), is modeled by the probabilistic-possibilistic Znumber method. Also, in multifarious cases, the performance of the proposed index is evaluated.It is shown how flexible resources like electrical storage systems (ESS), thermal storage systems (TSS), electrical demand response programs (EDRP), and thermal demand response programs (TDRP) can increase the flexibility of the EH. It is also conducted that how the flexibility enhancement can increase construction costs.