Various methods based on hyperelastic assumptions have been developed to address the mathematical complexities of modeling motion and deformation of continuum manipulators. In this study, we propose a quasistatic approach for 3D modeling and real-time simulation of a pneumatically actuated soft continuum robotic appendage to estimate the contact force and overall pose. Our model can incorporate external load at any arbitrary point on the body and deliver positional and force propagation information along the entire backbone. In line with the proposed model, the effectiveness of elasticity versus hyperelasticity assumptions (neo-Hookean and Gent) is investigated and compared. Experiments are carried out with and without external load, and simulations are validated across a range of Young's moduli. Results show best conformity with Hooke's model for limited strains with about 6% average normalized error of position; and a mean absolute error of less than 0.08 N for force applied at the tip and on the body, demonstrating high accuracy in estimating the position and the contact force.