In this work, a novel Integrated-optical serially coupled microring resonator-based mechanical pressure sensor is reported. Finite-Difference-Time-Domain ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">FDTD</i> ) approach is used to build, analyze, and optimize <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$5\mu \text{m}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$4\mu \text{m}$ </tex-math></inline-formula> microring resonators(MRs). These optimized <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MRs</i> are used in the design and analysis of a serially coupled microring resonator ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SCMR</i> ). The <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SCMR</i> is used as a sensing element in the pressure sensor. To experience the maximum stress, the sensing element is integrated with the square-shaped mechanical diaphragm. The stress of this diaphragm is analyzed by Finite-Element-Method of COMSOL Multiphysics and the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">FDTD</i> method of Ansys Lumerical simulation tool is used for the analysis of the field propagation through the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SCMR</i> . The Photo-elastic effect is the working principle of this device. The dimensions of this sensor are <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$25\times 25\mu \text{m}^{2}$ </tex-math></inline-formula> . A sensitivity of 0.34nm per 0.1 MPa, FSR of 94nm, and a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q-factor</i> of 21514 are reported. The sensor can be used to measure the applied pressure range of 0 to 600 kPa. A microring resonator of radius <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$5\mu \text{m}$ </tex-math></inline-formula> is fabricated and characterized at an operating wavelength of 1550nm.