The nation-wide strike call, demanding early wage revision among other issues, was given by United Forum of Bank Unions (UFBU) that comprises nine national unions.
It was, however, business as usual at private sector banks like ICICI Bank and HDFC Bank.
Employees of public sector insurance companies, including LIC and New India Assurance, participated in the strike.
Apprehending disruption in normal operations, many public sector banks had already informed customers about the strike.
Sources said banks have taken steps to ensure that public do not face problems at least on the cash front during the strike period. Banks have replenished ATMs to meet the requirements in these two days.
Despite these measures, some ATMs went dry at commercial hubs.
All India Bank Employees Association (AIBEA) General Secretary C H Vekatachalam claimed clearing operations, electronic fund transfers, forex transactions and money market operations were completely disrupted across the country.
Bank unions are pressing for early wage revision of employees, which they said is due from November 2012. They are also opposing banking sector reforms and any plan for merger of banks.
There are 26 public sector banks with employees strength of around 10 lakh.
In the financial capital, Mumbai, normal operations were hit due to the strike.
"We have received massive response to our strike call and operations in banks and insurance companies are completely shut," All India Banks Employees Association Vice President Vishwas Utagi claimed in Mumbai.
Reserve Bank operations were unaffected even though Grade III and IV employees joined the two-day strike.
In December 2012 also, four bank unions went on strike opposing amendments carried out in the Banking Regulation Act and Banking Companies Act, enabling foreign equity in public sector banks.
The bank strike is part of a general strike call given by 11 central trade unions, including Indian National Trade Union Congress (INTUC), All India Trade Union Congress (AITUC), Bharatiya Mazdoor Sangh (BMS), Centre of Indian Trade Unions (CITU) and All India United Trade Union Centre.