This article presents a methodology for estimating the gripping forces in a Fin Ray-type gripper, based on the integration of experimental and computational approaches. The development and validation methods includes (1) mechanical modeling and material selection; (2) experimental tests to relate FG finger displacement to maximum applied force using a load cell; (3) validation of the computational model through finite element method (FEM) simulations in ABAQUS using experimental data; and (4) experimental analysis of the FG handling a chicken egg, with the FEM determining the stress applied to the egg. The computational results showed a maximum stress of approximately 7 MPa on the egg, with no signs of damage, demonstrating the FG's suitability for handling delicate objects in both the experimental and computational procedures, thus enabling safe object handling without causing damage. This work advances research on Fin Ray-type flexible end-effectors, emphasizing their utility in manipulating fragile objects without requiring complex force and pressure control algorithms.