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Operational flexibility is an important attribute for the design of sustainable power systems with a high share of intermittent renewable energy sources (IRES). Resilience against extreme weather is also becoming an important concern. In this study, a modeling and optimization framework for power systems planning, which considers both operational flexibility and resilience against extreme weather events, is proposed. In particular, a set of piece-wise linear models are developed to capture the impact of extreme heat waves and drought events on the performance of the power generation units and on the system load. A method is, also, proposed to incorporate the impact models within a modified optimal power system planning problem that can adequately accommodate high shares of IRES. The framework is applied to a case study based on real future climate projections from the Coupled Model Intercomparison Project phase 5 (CMIP5) under different levels of IRES penetration (up to 50%) and severity of the extreme weather events. A sensitivity analysis is conducted for planning under different Representative Concentration Pathways (RCPs) that cover the impact of different trajectories of greenhouse gas concentration on future climate. In particular, RCPs with increase in radiative forcing of +8.5 Wm(-2), +4.5 Wm(-2) and +2.6 Wm(-2) of the pre-industrial levels are considered. The results demonstrate that significant improvements in terms of load supply under an extreme heat wave and drought events can be achieved following the resilient planning framework proposed, compared to conventional planning methods. It is also shown how renewable generation units can improve the system performance against those extreme climate events. Moreover, the quantitative assessment indicates an important interaction between the resilience of the system and its flexibility, and the compound impact of failing to consider either aspect in the power system design phase.