This paper presents a number of parallel algorithms for the dynamic programming problem Sequential algorithms run in O(n ³) time or, if the quadrangle inequality holds (cf. [7]), in O(n ²) time. For the former we design parallel algorithms that run in O(n ³/p) time on p<n ² processing elements (PEs). It is also shown that dynamic programming problems satisfying the quadrangle inequality can be solved in O(n ²/p+n log p) time using p (1<pn) PEs. A global shared memory is assumed. Moreover, we design a systolic array for computing the c(i,j)'s that runs in linear time using p (n ²) PEs.