This paper presents a theoretical model for the shape reconstruction of soft robots subjected to a tip force and a tip moment as well as a distributed load along the body. The distributed load may be the reminiscent of blood flow force acting on ablation catheters in the left atrium. The model is developed based on the Euler-Bernoulli beam theory and approximation of the shape via a cubic Bézier curve. The model is validated against a finite element model, where the maximum relative error is below 5%. Despite the reasonable accuracy, the model's average refresh rate (~ 1.1 Hz) is way below the acceptable rate for clinical applications, which in turn poses a challenge to the use of the model in such applications. To address this, a novel model based on the Bayesian neural network (BNN) is developed for the shape reconstruction. The data required for training, validation and testing this NN model is created using the theoretical model and considering a suitable range of tip force, tip moment and distributed load. The model is shown to be very accurate and with an average refresh rate of 50 Hz, which makes it ideal for clinical operations. Since in many soft robotic applications, such as minimally invasive surgery, tip force estimation is crucial, a new BNN model is developed to estimate the tip force given that the deformed shape, tip moment, and the distributed load are known. The data collected from solving the theoretical model is re-arranged and used for training, validation and testing the force estimation NN model. This model is validated against a set of in vitro experimental results collected from a one-of-a-kind apparatus used to simulate interactions between blood flow and ablation catheters. A fair agreement between the two sets of results is observed. The present study highlights the great potential of NN models for shape reconstruction and force estimation of soft robots, particularly for the use in minimally invasive surgery.