Let us start by defining nihilism. Nihilism is the philosophical belief that negates purpose and meaning in life by presenting life as fundamentally meaningless and without any value. Given this definition, we can see that nihilism is an approach that is actually very strong in the majority of Kafka's short stories. In particular, however, you might like to consider "The Metamorphosis" and the poor life of Gregor Samsa. The irony is that Gregor's life seems actually to improve in some ways by his transformation into an insect. Note how he thinks of his life as a human, working as a travelling salesman:
"Oh God," he thought, " what a strenuous profession I've picked! Day in, day out on the road. It's a lot more stressful than the work in the home office, and along with everything else I also have to put up with these agonies of traveling--worrying about making trains, having bad, irregular meals, meeting new people all the time, but never forming any lasting friendships that mellow into anything intimate. To hell with it all!"
If we examine Gregor Samsa's life and the way that he has to work so hard to support his family we can see a life that is essentially based around lack of purpose and meaninglessness. The way that after his transformation Gregor's family slowly change their opinion about him until he is forgotten completely and dies alone makes this powerful story a tremendous allegory about nihilism in our contemporary nihilistic society.