The diversity of spatial modes present within a multimode fiber has been exploited for a wide variety of imaging and sensing applications. Here, we show that this diversity of modes can also be used to perform quantitative strain sensing by measuring the amplitude of the Rayleigh backscattered speckle pattern in a multimode fiber. While most Rayleigh based fiber sensors use single mode fiber, multimode fiber has the potential to provide lower noise due to the higher capture fraction of Rayleigh scattered light, higher non-linear thresholds, and the ability to avoid signal fading by measuring many spatial modes simultaneously. Moreover, while amplitude measuring single mode fiber based Rayleigh sensors cannot provide quantitative strain information, the backscattered speckle pattern formed in a multimode fiber contains enough information to extract a linear strain response. Here, we show that by tracking the evolution of the backscattered speckle pattern, the sensor provides a linear strain response and is immune to signal fading. The sensor has a noise floor of 2.9 pɛ/√Hz, a dynamic range of 74 dB at 1 kHz, and bandwidth of 20 kHz. This work paves the way for a new class of fiber optic sensors with a simplified design and enhanced performance.