DMA architectures capable of performing multi-level multi-striding and determining multiple memory addresses in parallel are described. In one aspect, a DMA system includes one or more hardware DMA threads. Each DMA thread includes a request generator configured to generate, during each parallel memory address computation cycle, m memory addresses for a multi-dimensional tensor in parallel and, for each memory address, a respective request for a memory system to perform a memory operation. The request generator includes m memory address units that each include a step tracker configured to generate, for each dimension of the tensor, a respective step index value for the dimension and, based on the respective step index value, a respective stride offset value for the dimension. Each memory address unit includes a memory address computation element configured to generate a memory address for a tensor element and transmit the request to perform the memory operation.