Not far from the tech campuses that have minted billionaires, residents in Silicon Valley have lost patience with homeless encampments that have sprouted along bike paths and parks in San Jose, Calif.

Mattresses, plastic bags and grocery carts have fallen into ravines and choked creeks whose shaded banks once drew hikers, cyclists and kayakers. San Jose closed an entire city park because hundreds of people posed a safety risk by living there permanently in recreational vehicles.

Homelessness along Skid Row in Los Angeles and in the Tenderloin in San Francisco has long defined the problem in California, but the most intense battles this year over encampments have emerged elsewhere in the state. Local leaders have vowed to take more aggressive steps, making use of a Supreme Court decision last year that empowered them to penalize people for sleeping on the street.

In San Jose, Mayor Matt Mahan, a Democrat, recently called for arresting homeless people if they refused shelter three times.

It’s rare for leaders in the liberal Bay Area to adopt such an approach, which critics say criminalizes homelessness. But his idea has drawn widespread support. While there remains opposition, interviews with residents, elected officials and advocates show that rising frustration with homelessness is making Silicon Valley voters desperate for action and leading them to proposals that once would have seemed too right-leaning for these heavily blue cities.