Quadrupedal robots possess the ability to move freely in the world and perform a variety of actions that would be unsafe or impractical for humans to perform. In the SNOW project, a quadrupedal robot is tasked with aiding firefighters in rescue missions during house fires by locating humans and assessing their health. Pushing away obstacles that cannot be circumvented otherwise is one of the many capabilities a quadrupedal robot should possess to be of most use in such missions. We develop a proof of concept by solving two problems sequentially: which stance to take on prior to the push and how to perform the push. The process of stance selection starts with generating a certain amount of stances. Stances are generated starting from a preselected stance appropriate to the goal location and deviating from the 12 joint angles with a normal distribution. All generated stances are ran through a number of filters, which rely on solving for the forward and inverse kinematics of the robot. These filters check if the initial position is sensible and balanced and if the projected final position is close to the goal and balanced. The inverse kinematics are solved using Adaptive-Network-Based Fuzzy Inference Systems (ANFIS), which results in accurate estimations within a time frame that can be used in real-time applications. The final stance is selected by comparing the total displacement of all joint angles per stance, where the lowest total displacement is considered optimal. The push is controlled by a nonlinear model predictive controller. We strive for a stable push, where the contact between the pusher and the object sticks, by keeping the movement of the end-effector within the motion cone. The motion cone denotes all twists the object can have without slipping at the contact with the pusher and is constructed using the limit surface to model the interaction between the object and the support surface and the generalized friction cone to model the interaction between the pusher and the object. We find that the motion cone predicts stick and slip with an accuracy slightly higher than 80%. Our controller steers accurately to all goals that lie within the motion cone and moves the object with a twist on the edge of the motion cone if the goal location lies outside of the motion cone. The robot remains balanced throughout the pushing motion in the vast majority of cases, but is more at risk of tipping over when pushing heavier objects.