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Flexible radio frequency (RF) circuits are highly desirable for flexible communication and other miniaturized function modules. However, the prevalent studies on flexible high-speed electronics have mostly focused on individual elements such as transistors, inductors, capacitors and transmission lines. Research on flexible RF monolithic integrated functional circuits is still limited. This letter presents the design of a flexible monolithic integrated silicon RF low noise amplifier (LNA) on plastic substrate. For the LNA, a flexible thin film transistor (TFT) based on a silicon nanomembrane, high-frequency flexible inductors and capacitors are fabricated and modeled. The impedance matching circuit on plastic substrate is analyzed and optimized. The LNA has a gain of ∼11 dB and a noise figure (NF) of ∼4.3 dB at 300 MHz. The influence of the parasitics induced by the flexible impedance matching on the gain and NF is discussed. This study provides useful design guideline for flexible RF monolithic integrated circuits and expands the high frequency applications of flexible electronics.