I guess this question is with reference to the modes of investment that are complaint with the Islamic Shariah as according to the Shariah the investment of money in interest bearing assets is not allowed.
The options of investment that are non-interest bearing and compliant with the Shariah include investment in the equity of companies involved in activities considered Halal. Here the gains made are due to capital appreciation and the dividends paid by the companies.
Another option is buying assets like real estate, machinery, etc and leasing them to others for their use.
Trading in commodities which do not violate the laws of the Shariah like wine, pork, etc. is also a permitted investment.
Each of the above mentioned options also have some rules that they have to adhere to for them to be Shariah compliant. More details are provided in the source given below.