A hypergraph H = (V, E), where V = {x(1),...,x(n)} and E subset of 2(V) defines a hypergraph algebra R-H = k[x(1),...,x(n)]/(x(i1)...x(ik); {i(1),...,i(k)} is an element of E). All our hypergraphs are d-uniform, i.e., vertical bar e(i)vertical bar = d for all e(i) is an element of E. We determine the Poincare series P-RH (t) = Sigma(infinity)(i=1) dim(k) Tor(i)(RH) (k, k)(t)(i) for some hypergraphs generalizing lines, cycles, and stars. We finish by calculating the graded Betti numbers and the Poincare series of the graph algebra of the wheel graph.